{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# python 符号处理 -- Sympy库"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "sympy 有 numpy 和 matplotlib 接口，可以实现数值处理和图形输出。 sympy 可以提供复杂的符号输出格式，进行计算机代数系统的符号计算。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## sympy 的基本使用"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 调用 sympy， anaconda已经默认安装"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function sympy.interactive.printing.init_printing(pretty_print=True, order=None, use_unicode=None, use_latex=None, wrap_line=None, num_columns=None, no_global=False, ip=None, euler=False, forecolor=None, backcolor='Transparent', fontsize='10pt', latex_mode='plain', print_builtin=True, str_printer=None, pretty_printer=None, latex_printer=None, scale=1.0, **settings)>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.init_printing #使用其他编译器的时候，如pycharm等需要输入这条命令。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 定义一个符号"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sy#导入sympy库\n",
    "sy.init_printing()#初始化sympy输出格式，使数学表达式的输出更美观\n",
    "x,y=sy.symbols(\"x y\")#定义符号变量x和y,这些变量在后续的表达式中使用\n",
    "D=(x+y)*sy.exp(x)*sy.cos(y)#exp是以e为底的指数函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left(x + y\\right) e^{x} \\cos{\\left(y \\right)}$"
      ],
      "text/plain": [
       "         x       \n",
       "(x + y)⋅ℯ ⋅cos(y)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D # 输出表达式， D不用再次定义"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 定义一个函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( f{\\left(x \\right)}, \\  f{\\left(x,y \\right)}, \\  g{\\left(x \\right)}\\right)$"
      ],
      "text/plain": [
       "(f(x), f(x, y), g(x))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f, g =sy.symbols(\"f g\", cls=sy.Function)#定义符号函数f和g\n",
    "f(x), f(x,y), g(x)#表示f是一个关于x的函数，表示f是一个关于x和y的函数，g是一个关于x的函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 定义变量的类型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(True, j**2, True, True, u**2)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy as sy\n",
    "\n",
    "# 定义符号变量 i 和 j，且它们都是整数类型\n",
    "i, j = sy.symbols(\"i j\", integer=True)\n",
    "\n",
    "# 定义符号变量 u 和 v，且它们都是实数类型\n",
    "u, v = sy.symbols(\"u v\", real=True)\n",
    "\n",
    "# 检查 i 是否为整数, 计算 j 的平方, 检查 j 的平方是否为整数, 检查 u 是否为实数, 计算 u 的平方\n",
    "i.is_integer, j*j, (j*j).is_integer, u.is_real, u*u\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 常用常数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( i, \\  e, \\  \\pi, \\  \\infty\\right)$"
      ],
      "text/plain": [
       "(ⅈ, ℯ, π, ∞)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.I, sy.E, sy.pi, sy.oo#定义特殊常量，虚数单位i2=-1，自然常数e=2.71828，圆周率pi=3.14159，无穷大"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 给变量带入值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle y \\cos{\\left(y \\right)}$"
      ],
      "text/plain": [
       "y⋅cos(y)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D0=D.subs(x,0)#替换，用0替换x，subs（old, new）\n",
    "D0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 向量，矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}1 & x\\\\y & 1\\end{matrix}\\right], \\  \\left[\\begin{matrix}u\\\\v\\end{matrix}\\right], \\  \\left[\\begin{matrix}u & v\\end{matrix}\\right], \\  \\left[\\begin{matrix}u + v x\\\\u y + v\\end{matrix}\\right]\\right)$"
      ],
      "text/plain": [
       "⎛⎡1  x⎤  ⎡u⎤          ⎡u + v⋅x⎤⎞\n",
       "⎜⎢    ⎥, ⎢ ⎥, [u  v], ⎢       ⎥⎟\n",
       "⎝⎣y  1⎦  ⎣v⎦          ⎣u⋅y + v⎦⎠"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy as sy\n",
    "x,y,u,v =sy.symbols(\"x y u v\")#定义符号函数xyuv\n",
    "M=sy.Matrix([[1,x],[y,1]])#定义一个矩阵M\n",
    "V=sy.Matrix([[u],[v]])#定义一个列矩阵\n",
    "VT=sy.Matrix([[u,v]])#定义一个行矩阵\n",
    "M,V,VT,M*V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left( \\left[ \\left( 1 - \\sqrt{x y}, \\  1, \\  \\left[ \\left[\\begin{matrix}\\frac{1 - \\sqrt{x y}}{y} - \\frac{1}{y}\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( \\sqrt{x y} + 1, \\  1, \\  \\left[ \\left[\\begin{matrix}\\frac{\\sqrt{x y} + 1}{y} - \\frac{1}{y}\\\\1\\end{matrix}\\right]\\right]\\right)\\right], \\  \\left[\\begin{matrix}1 & y\\\\x & 1\\end{matrix}\\right], \\  - x y + 1, \\  \\left[\\begin{matrix}\\frac{1}{- x y + 1} & - \\frac{x}{- x y + 1}\\\\- \\frac{y}{- x y + 1} & \\frac{1}{- x y + 1}\\end{matrix}\\right], \\  \\left[\\begin{matrix}- \\frac{x y}{- x y + 1} + \\frac{1}{- x y + 1} & 0\\\\0 & - \\frac{x y}{- x y + 1} + \\frac{1}{- x y + 1}\\end{matrix}\\right]\\right)$"
      ],
      "text/plain": [
       "⎛⎡⎛                ⎡⎡      _____    ⎤⎤⎞  ⎛                ⎡⎡  _____        ⎤⎤⎞\n",
       "⎜⎢⎜                ⎢⎢1 - ╲╱ x⋅y    1⎥⎥⎟  ⎜                ⎢⎢╲╱ x⋅y  + 1   1⎥⎥⎟\n",
       "⎜⎢⎜      _____     ⎢⎢─────────── - ─⎥⎥⎟  ⎜  _____         ⎢⎢─────────── - ─⎥⎥⎟\n",
       "⎜⎢⎜1 - ╲╱ x⋅y , 1, ⎢⎢     y        y⎥⎥⎟, ⎜╲╱ x⋅y  + 1, 1, ⎢⎢     y        y⎥⎥⎟\n",
       "⎜⎢⎜                ⎢⎢               ⎥⎥⎟  ⎜                ⎢⎢               ⎥⎥⎟\n",
       "⎜⎣⎝                ⎣⎣       1       ⎦⎦⎠  ⎝                ⎣⎣       1       ⎦⎦⎠\n",
       "⎝                                                                             \n",
       "\n",
       "⎤                    ⎡   1        -x    ⎤  ⎡    x⋅y         1                 \n",
       "⎥                    ⎢────────  ────────⎥  ⎢- ──────── + ────────            0\n",
       "⎥  ⎡1  y⎤            ⎢-x⋅y + 1  -x⋅y + 1⎥  ⎢  -x⋅y + 1   -x⋅y + 1             \n",
       "⎥, ⎢    ⎥, -x⋅y + 1, ⎢                  ⎥, ⎢                                  \n",
       "⎥  ⎣x  1⎦            ⎢  -y         1    ⎥  ⎢                           x⋅y    \n",
       "⎦                    ⎢────────  ────────⎥  ⎢          0            - ──────── \n",
       "                     ⎣-x⋅y + 1  -x⋅y + 1⎦  ⎣                         -x⋅y + 1 \n",
       "\n",
       "          ⎤⎞\n",
       "          ⎥⎟\n",
       "          ⎥⎟\n",
       "          ⎥⎟\n",
       "     1    ⎥⎟\n",
       "+ ────────⎥⎟\n",
       "  -x⋅y + 1⎦⎠"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.eigenvects(), M.T, M.det(), M.inv(), M*M.inv()#计算矩阵的特征值和特征向量，计算矩阵的转置，计算矩阵的行列式，计算矩阵的逆，计算矩阵与其逆矩阵的乘积"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## sympy 执行常用数学计算"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 求解一元一次方程\n",
    "\n",
    "$5*x+20=100$\n",
    "\n",
    "要写成  ***=0 的形式，  用solve函数求解方程"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{x: 16}\n"
     ]
    }
   ],
   "source": [
    "x = sy.symbols('x')#定义一个符号变量\n",
    "answer=sy.solve([5*x+20-100],[x])#该函数的第一个参数是一个包含待解方程的列表，第二个参数是要解的变量列表\n",
    "print (answer) # 不能省略乘号，solve() 函数会返回一个列表，其中包含解的值。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "solve 是通用的解方程的函数，对于单变量方程，还可以使用solveset()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{16\\right\\}$"
      ],
      "text/plain": [
       "{16}"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.solveset(5*x+20-100,x)#solveset() 函数将返回一个集合，包含所有解。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAE4AAAAUCAYAAAAjvwuMAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAABJ0AAASdAHeZh94AAACgUlEQVR4nO2YT4hNYRjGf9co1GDMSjbKQsif8SclDYPUlIVZsEFJFtj4U7IZee6zsvGn2JDNFErJwsJCFmajJMpiRDOpq4wUUmOEBtfinJM759573DvuuffKPHV7z/3e97zf8z29fd97vkw+n2cS1WNKown8q5ia5LS9CzgMLAZagdWSntaBV8NgOwv0Ah+Ah8AJSYPxuLLC2V4CXAM+AzeBYeBtCkR3ABuBDmAFMBO4LmlPg3L3A9PDd7YD84C18aCkitsEZIBeSRcmwLtSnCRY1CjwGljUyNyS+gnEw/YTYI3tVkmjhXFJe1x7aJ9Xz7cqHAMWArOAQ02W+wVB8cyJO5IqriW0YxOYsGJIuh8922623NHaW+KOyVN1gkgSri20X+rAo1nxNbSz446SwtnOAJ1AHniVHq+mRy60XXHHuD3OdjewFdgArAIuSyrbgtjOAfOrIFKTNqOOuAocBM7YXg8MAVck5eKHQzdwJHweAC7+IfFLfpdzJXhTRWzDIWnY9mngPLAzHL4HjBdO0lHbpwh6uBvAXdvzJf0ok3hLirwbDtvbgEvAA+AAMChpDEq0I5JGgNu2bwG7CT63BupHt6mwObRZSc8KHUl9XHQotCfENAS2+4C9wD5JfSlOFTW+ubgjSbio+Uu117PdA/SEf+eGdl0oDsB7Scdjr0WcvqeQu6J5koSr10VdB0H1FGJB+IOg8uOLWwZ8Au6kkLsUirRIEu5baIu+02oJSVkgW2m87TZgOXBW0sda5i6BaO1FnUOScEOh3W/7MTAs6edfkKgVOgm2kXNpTWB7GsGtShcwAryLx2TKXZ3bngE8ApYWDK/8Ty4yVTCUlVR0Q/ALmXnGGWVxZNAAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle \\left\\{-1, 1\\right\\}$"
      ],
      "text/plain": [
       "{-1, 1}"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.solveset(x**2-1,x)#该函数的第一个参数是要解的方程，第二个参数是待解的变量。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 求解二元一次方程组\n",
    "\n",
    "$3*x+ 4*y=49 $\n",
    "\n",
    "$8*x-y=14$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{x: 3, y: 10}\n"
     ]
    }
   ],
   "source": [
    "x, y = sy.symbols('x y')\n",
    "answer = sy.solve([3*x+ 4*y-49, 8*x-y-14],[x,y])#该函数的第一个参数是一个包含待解方程的列表，第二个参数是一个包含待解变量的列表。\n",
    "print (answer) # 不能省略乘号"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "线性方程可以利用 linsolve() 求解."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGAAAAAUCAYAAAByKzjvAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAABJ0AAASdAHeZh94AAAFVElEQVR4nO2Ze4hVVRTGf6NRWmqaolIhZjZqT6uhNNPe44BFUvZPqL0fGJjVFJTBN5+kJZWR9n6AWEEWQ0oPyorEUHqYSpiaJthDTC1FU7TMpj/2PuN07rnn3hmdFOoDWcNZa+2979p7Pa1oaGjgfxw8tDnYB/iv47A8pu1rgfHAAKADcLakZRlys4Aa4ARJO1vhnIcUbJ8NLAZulvRyEZk6YCLwK/AZcJ+k1Wm5ohdg+2TgVWAn8CawHvg5Q64KGA3Upo1veypQBVQC3YBdwPfAHOApSb/m/9Tmw/Yo4AJgIHAG0BF4TdLoEnrHA5MID6krsCGe05K2NpWV9JXtOcBDtmdL2pGx5HygXTzHlcCxwDlpoTwPuAioACZKmp4jNwXYDjybwbsLWAJ8CGwCjgIGAXXArbYHSfoxZ+2W4EGC4XcAPwH9SynYPhFYBHQH5gKrCMa6E6ixPSTjsTwMfE6IEFPSa0qaT7gEbH8FVNnukL6svAs4JtKVOQevBC4FXpK0K0Okk6TdGXqTgQeA+4FxOWdoCe4iGP47gid8UobOMwTjj5c0o8k5p8X1JgO3N1WQ9IXtVcBttqdK2puz/irgLKAL4WE0Ii8Jt410T47MjQQvmZ3FzDJ+xBuRnpSzdosg6RNJaySVVd7Z7gNUA+uAp9PLEULwGNtHZai/DvQiPMI8JDZsm2bsbxV0KbCXkGSagysi/Xo/9z8QuDjSeZL+asqQ9BuwEDiSEDrTWBjpZS3dPC8EdY40K7QQX8RAYGWpysd2LaGKOpqQlM8nGP+R5h23VdAv0oIKJWINwUMqgY9TvC8jHVZijyQSHJ1mZHqA7QpgKNBAqFqycBzBpTaU2BygluDOEwjGfx+olrS5DN3WRmKUbUX4yffOaYakbQTj9iqxx7pIL0wz/uEBtmsI7jSMkDSel1RQekZ0jXRrEX7Tg/aM6/cAziO8/KW2L5e0pJT+QUZFpMVyyhagR4k1XiEk8cdsDyF41YuS1qU9oAa4mxAmlgMzKI4kNLUrsXkjJG2U9BbBpbsCs8rVbUUkL7wgPER0Ssml0Z4iYTqBpPWEsnUPcA2hAuwNqRAkaUI8yEigL/CB7YLMHbEp0q5F+HkH+h5YAZxiu1tz9Q8wvo20sgg/qdQKcoTtNoTQtCnNS8mNAJ4j9ESnAofHPqEwB0jaLmkuUE+I8wOKrLsB2My+JNZcHBtpXv38byDpE6qjQRthuyMwhPDCsyq9foQQtazEHkmlVSfpG0mNpX1eGZok32OymLHOXgB0s903zbfd33bPjO9tYiPWHViUbvNtz7TdYPv6vF90oCBpLTCPEBLuSB+X0L3PKlLpJaVpqWavS6Tr0oy8MjS5pbxLqgeuBoYTOs+mqAEetb0AWEsYSvUgdKd9CHOlWzLWTPb7M2fforA9khBCAZIHMNj2zPj3L5JqU2rjCKOI6bYvIXT/5xLGMasJQ7UsVBM8eG6JYxX9TXnGLaeTrAc2AmMzeB8BLxByxFXAvYTL2kJ4WadIWpGhdxrwG/BuGftnYSBwXfw3PH7r0+TbqLRC9IIqYCbB8PcAJwLTgcFZQ0PbSa58pxnzrAKb5nnA75F2KSYg6Q/bTwJTbJ8paWkT3nIKXToXtjsDpwOPp0NTuZBURxj2NVfvR+CGZqiMJVSAj5chm9iwYDSTdwFrIr3J9mJgfbpVj3iCUONOYt+IoaUYSgh90/ZznVaF7faEQWK9pE9z5I4gTGYvJEyMCxrPvBD0HqEXGAH8AOy1PTAtFAduY4DFRQZWZUPS25La5TR/hwp6E8JrOpc0Iv6HzG7CyLoTMC3rAf8NPu62VDSwj1MAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle \\left\\{\\left( 3, \\  10\\right)\\right\\}$"
      ],
      "text/plain": [
       "{(3, 10)}"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eqns=[3*x+ 4*y-49, 8*x-y-14]#这行代码定义了一个包含两个方程的列表 Eqns。\n",
    "sy.linsolve(Eqns,[x,y])#这行代码调用 sy.linsolve()函数来求解线性方程组。该函数的第一个参数是包含方程的列表，第二个参数是待解的变量列表。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以写成矩阵形式求解（参考PPT）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{\\left( 3, \\  10\\right)\\right\\}$"
      ],
      "text/plain": [
       "{(3, 10)}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A=sy.Matrix([[3,4],[8,-1]])#这行代码定义了一个 2x2 的系数矩阵 \n",
    "b=sy.Matrix([[49],[14]])#这行代码定义了一个 2x1 的常数项向量 \n",
    "sy.linsolve((A,b),[x,y])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "利用方程组的解，可以进一步求其他函数\n",
    "\n",
    "已知 $x + y =0.2, x + 3y = 1$  求 $x^2+4xy+4y^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.360000000000000\n"
     ]
    }
   ],
   "source": [
    "import sympy as sy\n",
    "x, y = sy.symbols('x y')#定义符号变量\n",
    "a = sy.solve([x + y -0.2, x + 3*y - 1],[x,y])#求解方程组\n",
    "x= a[x]#提取方程组的解\n",
    "y= a[y]#这两行代码从字典 a 中提取 x 和 y 的解，并重新赋值给 x 和 y。根据上一步的示例，x 和 y 将分别被赋值为 0.1。\n",
    "formula= x**2 + 4*x*y + 4*y**2   # ** 代表乘方, 字符之间不能省略乘号\n",
    "print(formula)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 求解积分， 使用integrate函数\n",
    "\n",
    "求解 $\\int_0^x \\frac{sin(t)}{\\pi-t} dt$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Si(x - pi) + Si(pi)\n"
     ]
    }
   ],
   "source": [
    "#参考PPT, untitled1\n",
    "import sympy as sy\n",
    "# 定义符号变量 t 和 y\n",
    "t = sy.Symbol('t')\n",
    "y = sy.Symbol('y')\n",
    "# 定积分的计算\n",
    "m = sy.integrate(sy.sin(t) / (sy.pi - t), (t, 0, x))\n",
    "# 输出结果\n",
    "print(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "二重积分\n",
    "\n",
    "$\\int_{0}^{\\pi} \\int_0^x \\frac{sin(t)}{\\pi-t} dt dx$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The value of the double integral is: 2\n"
     ]
    }
   ],
   "source": [
    "import sympy as sp\n",
    "\n",
    "# 定义变量和函数\n",
    "x, t = sp.symbols('x t')\n",
    "expr = sp.sin(t)/ (sp.pi - t)\n",
    "\n",
    "# 计算积分\n",
    "result = sp.integrate(expr, (t, 0, x))  # 对 t 从 0 到 x 积分\n",
    "result = sp.integrate(result, (x, 0, sp.pi))  # 对 x 从 0 到 pi 积分\n",
    "\n",
    "# 打印结果\n",
    "print(\"The value of the double integral is:\", result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 微分方程 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "求微分方程，使用dsolve() 函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 函数微分"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 微分方程"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(x + y)*exp(x)*cos(y)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left(x + y\\right) e^{x} \\cos{\\left(y \\right)} + e^{x} \\cos{\\left(y \\right)}$"
      ],
      "text/plain": [
       "         x           x       \n",
       "(x + y)⋅ℯ ⋅cos(y) + ℯ ⋅cos(y)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy as sy\n",
    "sy.init_printing()#初始化输出格式\n",
    "x,y=sy.symbols(\"x y\")#定义符号变量\n",
    "D=(x+y)*sy.exp(x)*sy.cos(y)#定义表达式\n",
    "\n",
    "print(D)#输出表达式 \n",
    "#sy.diff 是 SymPy 中的求导函数。D 是你要对其求导的表达式,x 是求导的变量\n",
    "sy.diff(D,x) #对表达式进行微分，计算表达式 D 对 x 的偏导数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$y'-3y=2$\n",
    "\n",
    "其中我们知道 $y'$　一般是 $y'(t)=\\frac{dy}{dt}$　的简写，　所以上式可以表达为"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle y{\\left(t \\right)} = C_{1} e^{3 t} - \\frac{2}{3}$"
      ],
      "text/plain": [
       "           3⋅t   2\n",
       "y(t) = C₁⋅ℯ    - ─\n",
       "                 3"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#参考PPT\n",
    "import sympy  as sy                                                                                        \n",
    "t = sy.symbols('t')#定义符号变量\n",
    "y = sy.Function('y')#定义函数:\n",
    "#在 sy.dsolve 中，sy.Derivative 用来表示微分方程的导数项。\n",
    "sy.dsolve(sy.Eq(sy.Derivative(y(t), t) -3*y(t), 2), y(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle y{\\left(t \\right)} = C_{1} e^{3 t} - \\frac{2}{3}$"
      ],
      "text/plain": [
       "           3⋅t   2\n",
       "y(t) = C₁⋅ℯ    - ─\n",
       "                 3"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.dsolve(sy.Derivative(y(t), t) -3*y(t)-2, y(t)) #这是之前介绍的方程简单的写法（只写方程的左半部分）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "另一种写法\n",
    "求初值问题\n",
    "\n",
    "$f'(x)+f(x)+f^2(x)=0,~f(0)=1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle f{\\left(x \\right)} = - \\frac{1}{2 \\cdot \\left(\\frac{1}{2} - e^{x}\\right)}$"
      ],
      "text/plain": [
       "          -1     \n",
       "f(x) = ──────────\n",
       "         ⎛1    x⎞\n",
       "       2⋅⎜─ - ℯ ⎟\n",
       "         ⎝2     ⎠"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy  as sy  \n",
    "f = sy.symbols('f', cls=sy.Function)#定义一个符号函数 f(x)，这里 cls=sy.Function 指定 f 是一个函数\n",
    "x = sy.symbols('x')#定义了符号变量 x\n",
    "eq = sy.Eq(f(x).diff(x,1)+f(x)+f(x)**2, 0)#定义了一个微分方程，使用 sy.Eq 来创建等式.f(x).diff(x, 1) 表示函数 f(x) 对 x 的一阶导数\n",
    "con={f(0):1}#定义初始条件,这里定义了初始条件 con，表示在 x = 0 时，f(x) = 1。\n",
    "exp=sy.dsolve(eq, f(x),ics=con)#sy.dsolve 函数来求解微分方程 eq，解的形式是关于 f(x) 的。使得解满足 f(0) = 1。\n",
    "exp#输出结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "求解微分，并对结果中初值导致的常数项进行代换，并画图："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eq(y(t), 1/(C1*exp(-t) + 1))\n",
      "Eq(y(t), 1/(1 + exp(-t)))\n"
     ]
    },
    {
     "data": {
      "image/png": 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abDYbiYmJJCUlERcX17hOcXExjzzyCKtXryYyMpL8/HyH55y7MZN5Xx3lwR9Fcd+I7g7fvoiVNIISt7RlyxZiYmKIjo7G29ub8ePHs3z58ibrLFmyhHHjxhEZeXaGhtBQx45ePtl3kj80XOv0zJg+Dt22iDNQQYlbysnJISIionHZZrORk5PTZJ2DBw9y+vRprrvuOoYMGcKCBQsclm9PTgm/eHM78eEd+Of4gbrWSdySdvGJWzJN85zHvjsbQ11dHenp6Xz66adUVlYyYsQIhg8fTq9evZqsl5qaSmpqKgAFBQU/OFtucSXJ87bS0a8Nc+5PwM9bb1NxTxpBiVuy2WxkZWU1LmdnZxMeHn7OOqNHj6Zdu3YEBwdzzTXXsHPnznN+15QpU0hLSyMtLY2QkJAflKu84XTyiho7bzyQSGiAbtcu7ksFJW4pMTGRjIwMMjMzqampYenSpSQlJTVZ57bbbuPLL7+krq6OiooKNm/eTJ8+LXcsyF5v8tib28nIL+eVewfTu3NAi21LxBVo34G4JS8vL2bOnMmoUaOw2+0kJycTHx/P7NmzAUhJSaFPnz6MHj2a/v374+HhweTJk+nbt2+LZXpp9X4+3Z/PH26L55peP2wkJtIaGOfbF/8tF31SRJpKSEggLS3tin/u7a1Z/Orfu7h/RDeeu63lSlDESZ33LCDt4hOx2KYjp/jt+7u5umcwz46Nu/QPiLgJFZSIhY6dOsPURelEdPJj5j2D8fLUW1LkP/RuELFIaVUtD85Po96EN+5PpEPbNlZHEnEqKigRC9TZ65m+ZDtHC88we8IQuge3szqSiNPRWXwiFnjho2/44mABM8b1Y0SPIKvjiDgljaBEHOzNLceZ99VRkq+KYvzQSKvjiDgtFZSIA20+copn39/DNb1CeGZMb6vjiDg1FZSIg2QVVTB18TYig/x4+e5BOmNP5BL0DhFxgDPVdTy0II1aez2vT0zQGXsil0EFJdLC6utN/uutHRw8WcasewYTHdLe6kgiLkEFJdLC/vHJQT7ed5Lf3hKnOfZEroAKSqQFrdiVy78+O8RdCTaSr+pudRwRl6KCEmkhe3JKePKdnSR068gfbu97zg0RReTidKGuuLz8/Hw2btxIbm4ubdu2pW/fviQkJODhYd2/v/LLqnhoQRpB7XyYfd8QfLw8Lcsi4qpUUOKy1q1bx4wZMygqKmLQoEGEhoZSVVXF+++/z+HDh7nzzjt54oknCAhw7I3/quvspCxMp7iilmVTRxDc3seh2xdpLVRQ4rJWrlzJa6+9RmTkubMx1NXVsWLFCtauXcsdd9zh0Fz//d4eth0v5pV7BxMf3sGh2xZpTXTDQnF5mZmZREVFXfIxR+jeux/cPoNHb+jJL2/q5fDti7go3bBQWqfzjZDuvPNOh+f44mABeSVVjIoP4/Ebejp8+yKtjXbxicvav38/e/fupaSkhHfffbfx8dLSUqqqqhyaJbPwDNOXbMPXy5P/vWsgHh46Y0/kh1JBics6cOAAK1asoLi4mA8//LDxcX9/f1577TWH5SitqmXy/K14eXrQLciPdj56W4k0Bx2DEpf39ddfM2LECEu2ba83mTx/K19mFLJo8jCm3zWKtLQ0S7KIuDAdg5LW5YUXXuD06dMXLKfPPvuMFStWtGiGv6w5wLoDBfw+KZ7h0brxoEhz0r4IcVn9+vVj7Nix+Pr6MnjwYEJCQqiqqiIjI4MdO3Zw44038swzz7TY9t/fnsPszw8zYXgkE4Z3a7HtiLgrFZS4rGXLlrFx40b+/Oc/ExoaSl5eHgEBAUyYMIHU1FTatm3bYtvekVXMr/69i2FRnfifW+NbbDsi7kwFJS4rPT2dY8eOsXjxYtatW9fkucrKyhYrqBMlVUxZkEZYgA+vThhCG914UKRFqKDEZaWkpDB69GiOHDlCQkJC4+OmaWIYBkeOHGn2bVbV2pmyMI0z1XUsfPAqOrXzbvZtiMhZOotPXN7UqVN59dVXW3w7pmny6NIdrNiVS+p9CdwUF3bOOgkJCTqLT+TK6Sw+aZ0cUU4Ar6w/zIc7c3lqVOx5y0lEmpcKSuQyfLz3BH9Zc4DbB4Yz9doeVscRcQsqKJFL2H+ilMff2sEAWwdm3NFfNx4UcRAVlMhFnCqvZvL8NPx9vUidmIBvG914UMRRdBafyAVU19lJWZROQVk1bz88grAAX6sjibgVFZTIeZimyTPv7mHr0dO8fPcgBkQEWh1JxO1oF5/IefzfF0f497ZsHruhJ7cOCLc6johbUkGJfMeavSd4afV+xvbvwuM36saDIlZRQYl8y97cEh5fuoP+tkD++rMBOmNPxEIqKJEG+aVVTJ6fRqBfG167b4jO2BOxmApK3Nbq1auJjY0lJiaGF/70Eg8tTKe4opbXJiYQ+q0z9rZu3YqnpyfLli2zMK2I+1FBiVuy2+1MmzaNVatWsXfvXuZ/Y2dXVjH/GD+Qvl07NFnv17/+NaNGjbIwrYh7UkGJW9qyZQsxMTFER0cz6/Oj1IYPYKhvHqPiOzdZ7+WXX+aOO+4gNDTUoqQi7ksFJW4pJyeHiIgIlqVn86/PDjEksIrgwh3nrPPee++RkpJiTUgRN6eCErdkmiZFbYJ5+t1dXBUTxK3hFXh854y9xx9/nJdeeglPz4ufLJGamkpCQgIJCQkUFBS0ZGwRt6L7QYlbWvbxBn718Ul6hAezbOpIXvnHXwF4+umnG9eJioriP++PwsJC/Pz8SE1N5fbbb7/g79X9oES+l/Nez6GpjsTtnCqv5p/ba6ivq+H5GzvT1tNk6dKlLFmypMl6mZmZjd9PmjSJsWPHXrScRKR5qaDErVTV2nloQRr5ZdX8angA9995K3a7neTkZOLj45k9ezaAjjuJOAHt4hO3UV9v8os3t7NyTx6v3DOYn/Tr0uzb0C4+ke9Ft3wX9/biym/4aHcez/ykT4uUk4g0LxWUuIU5GzJ5fUMmk0Z2Z/LVUVbHEZHLoIKSVm/l7jxe+Ggfo+M78+zYOE0AK+IiVFDSqm09WsTjb+1gcGRH/jF+IJ4eKicRV6GCklbrUH45k+enYevYltcnJmh2chEXo4KSVimvpJKJczbTxtOD+Q8MpWM7b6sjicgVUkFJq1NcUcPEOVsorapj3gOJRHTyszqSiHwPKihpVSpq6kiet5Vjpyp4bWJCk1tniIhrUUFJq1Frr+eRxdvYkVXMv+4eyIgeQVZHEpEfQFMdSatQX2/yq2W7WH+ggD+N68fovroQV8TVaQQlLs80Tf648hve257Dkzf34u6hkVZHEpFmoIISl/evTw8xp2GWiGk/jrE6jog0ExWUuLTXvjjC3z85yB2DbfxOs0SItCoqKHFZizYd448rv+GWfl146Y5+eGiWCJFWRQUlLundbdk8u3wP1/cO5e8/H4iXp17KIq2N3tXiclbtzuPJd3YyIjqIV+4djLeXXsYirZHe2eJS1h3I59Gl2xkYEchrml9PpFVTQYnL+OpQISkL04nt7M/cB4bSzkeX8Ym0ZioocQkbDxXywLytdA9qx4LkYXRo28bqSCLSwlRQ4vQ2ZBSSPG8rUcHtWPLQMDppZnIRt6CCEqf2ZUYBD84/W06LJw8jqL2P1ZFExEG0E1+c1hcHC3hoQVrDyGm4Rk4ibkYFJU7pP+UUHdKexZO1W0/EHWkXnzidtftOMlnlJOL2VFDiVN7fnkPKonT6dAlgicpJxK1pF584jYWbjvG75XsYFtWJ1+9PpL2ucxJxa/oEEKfwyvpD/Hn1AW7sE8rMewZrhggRUUGJtUzT5KXVB5j9+WGSBoTzt7sG0EYTv4oIKiixUH29ye8+2MOiTce5d1gkz9/WF0/dMkNEGqigxBJVtXaeeHsnH+3O4+Fro/nN6N662aCINKGCEocrrqjhoQVpbD16mmfG9GbKNT2sjiQiTkgFJQ6VVVTBpLlbyCqq5OW7B3HrgHCrI4mIk1JBicPsySnhgXlbqa61s/DBoQyLDrI6kog4MRWUOMT6A/lMW7yNQD9vlkweRs8wf6sjiYiTU0FJizJNkzkbMnlx5Tf07hzA3AcSCQvwtTqWiLgAFZS0mOo6O//93h7eSc9mdHxn/nbXAN0FV0Qum66IlBZRUFbNPa9t5p30bB69oSev3DvY6cpp9erVxMbGEhMTw4wZM855fvHixfTv35/+/fszcuRIdu7caUFKEfflXJ8Y0irszS3hoflpFFXUMOuewdzSv4vVkc5ht9uZNm0aa9euxWazkZiYSFJSEnFxcY3rREVF8fnnn9OxY0dWrVrFlClT2Lx5s4WpRdyLRlDSrFbtzuPOV7/GBJaljHTKcgLYsmULMTExREdH4+3tzfjx41m+fHmTdUaOHEnHjh0BGD58ONnZ2VZEFXFbGkFJs6i11/PSqv28viGTQZGB/N99Qwj1d96TIXJycoiIiGhcttlsFx0dzZkzh5/85CeOiCYiDVRQ8oPlFlcyfck2th0vZtLI7jw9pjc+Xs49G7lpmuc8dqGpltatW8ecOXPYsGHDeZ9PTU0lNTUVgIKCguYLKeLmVFDyg6w7kM8v39pBrd1k5j2DGNvfNWaGsNlsZGVlNS5nZ2cTHn5u9l27djF58mRWrVpFUND5LyyeMmUKU6ZMASAhIaFlAou4IR2Dku+lzl7PX9bs54G5WwkL8OWD6Ve5TDkBJCYmkpGRQWZmJjU1NSxdupSkpKQm6xw/fpxx48axcOFCevXqZVFSEfelEZRcsfzSKh5dup1NR4r4eUIEz90W73I3GPTy8mLmzJmMGjUKu91OcnIy8fHxzJ49G4CUlBSef/55Tp06xSOPPNL4M2lpaVbGFnErxvn2xX/LRZ8U97Nqdx7PvLebylo7L9zejzuH2KyO5FQSEhJUYiJX7rwHgDWCkstSWlXL7z/Yy7vbcujXtQN///kAYkI1n56ItBwVlFzS14dP8eQ7OzlRWsWjN/TkF9fH6LbsItLiVFByQVW1dv665gBzNmbSPagdy1JGMCiyo9WxRMRNqKDkvHZlF/PkOzs5eLKcCcMjeWZMH/y89XIREcfRJ440UV5dx98+PsD8r44S4u/D3AcS+XFsqNWxRMQNqaCk0Sf7TvK75XvIK61iwrBuPDU6lgDfNlbHEhE3pYIS8kur+P2He1m5+wSxYf68fM9ghnTTsSYRsZYKyo3V2utZ+PUx/r72INX2ep4aFctDV0fj7aUz9ETEeiooN7X+QD5/WLGPwwVnuLpnMM/f1peo4HZWxxIRaaSCcjOHC8p5YcU+1h0ooHuQH3PuT+D63qEXnMlbRMQqKig3UVxRw8zPDjHvq6O0bePJM2N6M2lklHbniYjTUkG1cuXVdczdkEnqF0cor6nj5wkRPHFzLCH+PlZHExG5KBVUK1VVa2fRpmO8sv4wRWdquCkujCdu7kXvzgFWRxMRuSwqqFam1l7PO2nZvPxZBnklVfwoJpgnbu6lKYpExOWooFqJqlo776Rnk/rFYbKKKhkcGcjf7hrAyB7BVkcTEfleVFAurqyqlsWbjzNnQyYFZdUMjAjk97fG68w8EXF5KigXlV9WxYKvjrHg66OUVtVxdc9g/jl+ICOig1RMItIqqKBczK7sYuZuPMqKXbnU1ZuMju/M1Ot60N8WaHU0EZFmpYJyATV19azZe4K5GzPZdryYdt6e3DusG/eP7K7ZH0Sk1VJBObEjBeW8tTWLZenZnDpTQ7cgP343No6fJdjw1yzjItLKqaCcTFWtnTV7T/DmluNsOlKEp4fBDb1DuXtoJNf0CsHTQ8eXRMQ9qKCcQH29yebMIt7fnsPK3XmUVdcR0aktT42K5WdDbIQG+FodUUTE4VRQFjFNk/0nyvhgZy7Lt+eQW1JFO29PRvftwrjBXRkRHYSHRksi4sZUUA5kmib78kpZtfsEK3fncaTwDJ4eBtf0DOY3Y/pwU58w2np7Wh1TRMQpqKBaWJ29nq1HT/PpNyf55JuTHD1VgYcBI3oE8eDVUYyK70xwe03cKiLyXSqoFlBSUcvnGQV8+s1J1h8ooKSyFm9PD4b3COLha3twc1wYQSolEZGLUkE1gzp7PTuyivkio5AvMwrYmVVMvQlB7by5KS6MG/uE8qOeIbT30V+3iMjl0ifm92CvN9mXW8qmI6f4+sgptmYWUVZdh4cBAyICmX59T67tFczAiI46LVxE5HtSQV2Gyho7u7KLSTt2mvRjpxsLCSA6pB23Dgzn6phgRvYIpoOfLqAVEWkOKqjvME2TY6cq2JldzM6sEtKPn2ZvTgl19SZwtpDGDujC8OgghkcHEaZrlEREWoRbF1R9vcmxogr25JSwN7eUvbkl7MouoaSyFgDfNh707xrIQ9dEMySyI4O7daRTO2+LU4uIuAe3Kajiihr2nyjjwImyhj9LOXiynPKGXXVtPA16hfkzOr4zAyMDGWALpFdYe7w8PSxOLiLinlpVQdXXm+SWVHKk4AyH8ss5XFDe+GdheU3jeoF+bYgN8+eOwV2JD+9AXHgAvcL88fZSGYmIOAuXK6iqWjvZpyvJOl1B9ulKjp86Q2ZhBcdOneFYUQU1dfWN6wb4ehET2p7re4cSE9qeXmH+9O4cQFiAj27qJyLi5JyqoEzT5NSZGvKKq8gtqSSvuJK8kipyS6rIaSik/LLqJj/j4+VB96B2RAW34/reoXRr+D4mtD3B7b1VRCIiLsohBVVdZ+dUeQ2F5dUUlldTUFZNYXkN+aVVnCyt5mRZFfml1eSXVVFrN5v8rLeXB106+BLeoS3XxYZg6+hHRKe2RHT0I6KTHyHtfTSpqohIK+SQghrxp88oOlNzzuMBvl6EBfgSGuDDsKhOhAb40jnAhy6BbQnv0JYugb4EtdMoSETEHTmkoH55Uy88PQyC2/sQ3N6b4PY+hPj74NtGM3eLdVavXs1jjz2G3W5n8uTJ/OY3v2nyvGmaPPbYY6xcuRI/Pz/mzZvH4MGDLUor4n4cUlAThndzxGZELpvdbmfatGmsXbsWm81GYmIiSUlJxMXFNa6zatUqMjIyyMjIYPPmzUydOpXNmzdbmFrEvei8anFLW7ZsISYmhujoaLy9vRk/fjzLly9vss7y5cuZOHEihmEwfPhwiouLycvLsyixiPtRQYlbysnJISIionHZZrORk5NzxeuISMsxTNO84JOjR482CwsLm2VDBQUFhISENMvvciRXzQ3KfjGnT5+mtLSUbt3O7n4+deoUZ86cITIysnGdjIwMunTpQvv27QE4ePAgNpsNPz+/c7L+531SXV3NwIEDWyx3S9LrxfFcNTc0b/b09PQ1pmmOPucJ0zQv9tVshgwZ0py/zmFcNbdpKvvFfPXVV+bNN9/cuPziiy+aL774YpN1pkyZYi5ZsqRxuVevXmZubu5Ff6+fn1/zBnUgvV4cz1Vzm2azZz9vB2kXn7ilxMREMjIyyMzMpKamhqVLl5KUlNRknaSkJBYsWIBpmmzatIkOHTrQpUsXixKLuB+nmklCxFG8vLyYOXMmo0aNwm63k5ycTHx8PLNnzwYgJSWFMWPGsHLlSmJiYvDz82Pu3LkWpxZxLw4rqClTpjhqU83KVXODsl/KmDFjGDNmTJPHUlJSGr83DINZs2Zd0e8MDg5ulmxW0OvF8Vw1Nzgm+0VPkgAu+qSINJWQkEBaWprVMURczXmnC9IxKBERcUqXKiijJb4Mw3jKMAwMwwhpqW00c94XDMPYbRjGTsMw1hqG0dXqTFeQ/a+GYRxoyP++YRgdrc50mbnvMgxjn2EYpmEYiVbnuczMP0lPT68wDOOwYRhPW53nCnLPNQyjwDCMvVZnucLckYZhrDcMY3/Da+VxqzNdQfa2hmFsNQxjV0P2563OdIX5vQzD2GEYxkfN9DvPy+EjKMMwIoCbgOOO3vYP8BfTNPubpjkQWAH8zuI8V2It0Nc0zf7AQeBpi/Ncrj3AOOALq4NcDsMwPIFZQD8gDrjbMIy4i/+U05gHnHsNivOrA54wTbMPMByY5kJ/59XA9aZpDgAGAqMNwxhubaQr8hjwTUtvxIpdfH8HfoULHd8yTbP0W4vtcK3sH5umWdewuAmwWZnncpmm+Y1pmgesznEFhgKHTNM8YppmDbAUuM3iTJfFNM0vgCKrc1wp0zTzTNPc1vB9GWc/MLtam+ryNFz7U96w2KbhyyU+VwzDsAG3AK+39LYcWlCGYSQBOaZp7nTkdpuDYRh/NAwjC7gX1xpBfVsysMrqEK1UVyDrW8vZuMiHZWtgGEZ3YBDgMrP5GobhaRjGDiAfWGuapqtk/wdnBxn1l1jvB2v208wNw/gE6Hyep34LPAPc3NzbbA4Xy22a5nLTNH8L/Lbh2MJ04H8cGvAiLpW9YZ3fcnaXyGJHZruYy8ntQs63H90l/kXs6gzDaA/8G3j8O3s7nJppmnZgoGEYgcB7hmH0NU1zj8WxLsowjLFAvmma6YZhXNfS22v2gjJN88bzPW4YRj8gCtjZcANCG7DNMIyhpmmeaO4cV+pCuc9jCfARTlRQl8puGMb9wFjgBvMS1xU40hX8nbuCbCDiW8s2INeiLG7DMIw2nC2nxaZpvmt1nu/DNM1iwzDWc/Y4oFMXFHAVkGQYxhjAFwgwDGORaZoTWmJjDtvFZ5rmbtM0Q03T7G6aZnfOvqEHO0M5XYphGD2/tZgE7Lcqy5UyDGM08GsgyTTNCqvztGJbgZ6GYUQZhuENjAc+sDhTq2ac/ZfuHOAb0zT/1+o8V8IwjJCGkROGYbQFbsQFPldM03zaNE1bw2f4eOCzlion0HVQl2uGYRh7DMPYxdldlI9ZHegKzAT8gbUNp4XOtjrQ5TAM46eGYWQDI4CPDMNYY3Wmi2k4EWU6sIazB+vfNk1zr7WpLo9hGG8CXwOxhmFkG4bxoNWZLtNVwH3A9Q2v7R0N/7J3BV2AdQ2fKVs5ewxqhcWZnM6lZpIQERGxhEZQIiLilFRQIiLilFRQIiLilFRQIiLilFRQIiLilFRQIs3EMIxAwzAesTqHSGuhghJpPoGACkqkmaigRJrPDKBHwwWjf7E6jIir04W6Is2kYUbtFaZp9rU6i0hroBGUiIg4JRWUiIg4JRWUSPMp4+zEvCLSDFRQIs3ENM1TwMaGme91koTID6STJERExClpBCUiIk5JBSUiIk5JBSUiIk5JBSUiIk5JBSUiIk5JBSUiIk5JBSUiIk5JBSUiIk7p/wFbTrH3xHoGngAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1b49ee72130>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy.plotting as syp #SymPy的绘图模块\n",
    "import sympy as sy#导入SymPy库\n",
    "\n",
    "t = sy.symbols('t')#定义一个符号变量t\n",
    "y = sy.Function('y')#定义一个函数y\n",
    "\n",
    "ex=sy.dsolve(sy.Eq(sy.Derivative(y(t), t)-y(t)+y(t)**2, 0), y(t))#求解微分方程，\n",
    "print(ex)#这行代码打印微分方程的解。解的形式通常会包含一个积分常数 c1\n",
    "\n",
    "ex1=ex.subs({sy.symbols(\"C1\"):1}) #对常数C1进行代换,这行代码对解中的积分常数 C1 进行代换，将其设为1\n",
    "print(ex1)#这行代码打印代换后的解。\n",
    "syp.plot(ex1.rhs, (t,-4,4))#ex1.rhs 获取代换后解的右侧表达式，即解的具体形式,绘制解的图像，横轴范围为 -4到4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 化简"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 函数展开"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x^{2} + 2 x y + y^{2}$"
      ],
      "text/plain": [
       " 2            2\n",
       "x  + 2⋅x⋅y + y "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy as sy\n",
    "x = sy.symbols('x')#定义符号 x \n",
    "y = sy.symbols('y')#定义符号 y\n",
    "ex1=(x+y)**2 #定义表达式 (x+y)^2\n",
    "ex1.expand()#展开表达式，expand()来展开表达式"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对于三角函数，需要特殊处理"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\cos{\\left(x + y \\right)}$"
      ],
      "text/plain": [
       "cos(x + y)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.expand(sy.cos(x+y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\sin{\\left(x \\right)} \\sin{\\left(y \\right)} + \\cos{\\left(x \\right)} \\cos{\\left(y \\right)}$"
      ],
      "text/plain": [
       "-sin(x)⋅sin(y) + cos(x)⋅cos(y)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.expand(sy.cos(x+y),trig=True)#这里使用了trig=True参数来指定对三角函数进行展开"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 函数化简 factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left(x + y\\right)^{2}$"
      ],
      "text/plain": [
       "       2\n",
       "(x + y) "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ex2=x**2+2*x*y+y**2#定义表达式 x^2 + 2*x*y + y^2\n",
    "ex2.factor()# .factor()来对表达式进行因式分解，进行函数化简"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 约分 cancel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "1\n"
     ]
    }
   ],
   "source": [
    "import sympy as sy\n",
    "\n",
    "# 定义一个符号矩阵 M\n",
    "M = sy.Matrix([[1, 2], [3, 4]])#定义矩阵M为一个2x2矩阵\n",
    "\n",
    "# 计算 M 与 M 的逆矩阵的乘积，并打印其第一行第一列的元素\n",
    "element = (M * M.inv())[0, 0]#矩阵M的逆矩阵M.inv()乘以M会得到单位矩阵，即[[1, 0], [0, 1]]\n",
    "#[0, 0] 指的是取矩阵的第 0 行、第 0 列的元素。在单位矩阵中，这个位置的元素是 1。\n",
    "print(element)  # 输出 1\n",
    "\n",
    "# 简化第一行第一列的元素并打印\n",
    "simplified_element = element.cancel() #虽然在这里cancel()方法没有实质性的效果，因为元素本身已经是最简形式的1。但如果元素是一个复杂的分数，cancel()方法会将其化简。\n",
    "print(simplified_element)  # 输出 1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(x + 1)/x\n"
     ]
    }
   ],
   "source": [
    "import sympy as sy\n",
    "\n",
    "# 定义符号\n",
    "x = sy.symbols('x')\n",
    "\n",
    "# 定义一个分数表达式\n",
    "expr = (x**2 - 1) / (x**2 - x)\n",
    "\n",
    "# 使用 .cancel() 方法简化\n",
    "simplified_expr = expr.cancel()\n",
    "\n",
    "# 打印结果\n",
    "print(simplified_expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x^{31} + x^{30} + x^{29} + x^{28} + x^{27} + x^{26} + x^{25} + x^{24} + x^{23} + x^{22} + x^{21} + x^{20} + x^{19} + x^{18} + x^{17} + x^{16} + x^{15} + x^{14} + x^{13} + x^{12} + x^{11} + x^{10} + x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1$"
      ],
      "text/plain": [
       " 31    30    29    28    27    26    25    24    23    22    21    20    19   \n",
       "x   + x   + x   + x   + x   + x   + x   + x   + x   + x   + x   + x   + x   + \n",
       "\n",
       " 18    17    16    15    14    13    12    11    10    9    8    7    6    5  \n",
       "x   + x   + x   + x   + x   + x   + x   + x   + x   + x  + x  + x  + x  + x  +\n",
       "\n",
       "  4    3    2        \n",
       " x  + x  + x  + x + 1"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#推导见PPT\n",
    "c=(x**32-1)/(x-1)#定义一个分数表达式\n",
    "c.cancel()# 使用 .cancel() 方法简化"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 化简simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAABJ0AAASdAHeZh94AAAAi0lEQVR4nO3SIQoCYRQE4E+xajYbxObewGjdYBTMRmGj8PgP4zkM3kMQjEb7Wv6wrC6sxeTACzO8YSbMoK5r32LUJCmlDVYosMQYp4jYdppwzM9P3LH4lDRs8QPmmGDfq15EnBtVuzxvSb3wN/3cNGgONqVUosx0ijWuuGTtERFVe3sFdi1tlg9uqF5xyRu/uhi7owAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle 1$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import * #从SymPy库中导入所有的功能。这种导入方式可以让你直接使用SymPy中的所有函数和类，而无需使用前缀sy。\n",
    "x, y, z, t = symbols('x y z t') #定义符号变量x, y, z, t。\n",
    "simplify(sin(x)**2 + cos(x)**2) # simplify()用于简化数学表达式"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## sympy 的画图"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "sympy可以针对符号进行画图， matplotlib针对数据画图。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy.plotting as syp  #导入SymPy的绘图模块后，"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "syp.plot3d()#syp.plot3d 是 SymPy 提供的绘制三维图形的函数。它可以用来绘制多变量函数的三维图像。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x11b626d6640>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy as sy\n",
    "import sympy.plotting as syp\n",
    "\n",
    "# 定义符号变量\n",
    "x, y = sy.symbols('x y')\n",
    "\n",
    "# 定义表达式\n",
    "f = sy.sin(x) * sy.cos(y)\n",
    "\n",
    "# 使用 SymPy 的 plot3d 函数绘制三维图形\n",
    "syp.plot3d(f, (x, -sy.pi, sy.pi), (y, -sy.pi, sy.pi), xlabel='x', ylabel='y', zlabel='f(x, y)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 直接函数画图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x11b626d6dc0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.plot(sy.sin(x),x,x-x**3/6,x-x**3/6+x**5/120, (x,-4,4), title='sin(x) and Taylor approximants')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x11b626a1d60>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy as sy\n",
    "#见PPT\n",
    "# 定义符号变量\n",
    "x = sy.symbols('x')\n",
    "\n",
    "# 使用 sympy.plot() 绘制 sin(x) 和 Taylor 近似\n",
    "sy.plot(\n",
    "    sy.sin(x),                  # 原始函数 sin(x)\n",
    "    x,                          # 线性函数 x\n",
    "    x - x**3 / 6,              # 第一次 Taylor 近似\n",
    "    x - x**3 / 6 + x**5 / 120, # 第二次 Taylor 近似\n",
    "    (x, -4, 4),                # x 的范围从 -4 到 4\n",
    "    title='sin(x) and Taylor approximants'  # 图形标题\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 参数画图"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{eqnarray}\n",
    "&~&(x,y)\\\\\n",
    "x&=&cos(\\theta)+\\frac{1}{2}cos(7\\theta)+\\frac{1}{3}cos(17\\theta)\\\\\n",
    "y&=&sin(\\theta)+\\frac{1}{2}sin(7\\theta)+\\frac{1}{3}sin(17\\theta)\\\\\n",
    "\\end{eqnarray}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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unry1NY0jOdWGNseEATAJlAm+P5jLvoxKXpnSnd4BxtcSoUGuYt7yYwB8d49xzu66IvcOCuLhkSH8nFjEtweMb5YiEol459YYAlyseXjNcepkSkObZKKTMQnUTU5eVTPvbU9ndKQ7c/r6GdqcS1BrtDz043Hyq2V8cWdvAl1tDG3SDcUTY8IYF+3Bm1vSOJxtfLMUO0tdod/aZiWv/pFqaHNMdDImgbqJ0WoFnll/CnMzMf+b1sMoE1CX/pXJvoxKXpvWnQHdjL+CQ1dDJBLx3m2xBLpY89CPyZTVyw1t0iVEezvw4IgQfj1ezK60ckObY6ITMQnUTcy6pEIScmv4v8lRRrnulJBbw6e7s5jZy5c5fU3FRDsKO0tzvry7NzKlhmfXnzLK9aiHRoQQ6m7LK3+kmkLPbyJMAnWTIlOqeX97Bj39Hbmtt6+hzbkEmVLNEz+fwM/ZmlemRhvanBueEHc7npsQwd6MStYlFhnanEuQSsS8ODmK/GoZKw/nGdocE52ESaBuUn44kk9Fo4LnJ0YapWvvo52ZFNW28O6tsdhaGF+y8I3I3f0D6BvkzGubUimpazG0OZcwLMyNIaGufLEn2yjzt0y0PyaBuglRqDV8sz+XQSEu9Ak0vqi91JIGvj2Qy5y+fvQNMj77blTEYhHv3hqDWivw2ibjDEhYMiKE6mYlvyQZ3yzPRPtjEqibkK2ny6hoVLBoaDdDm3IJgqB7OTpYmfPc+EhDm3PTEeBiw6JhwWw5XUZyQa2hzbmEfkHOxPo58vX+HLSm/lE3PCaBugnZcLwYbwdLBoe4GtqUS9iTUcnhnGoeGRliyncyEPcPCcbVVspbm9OMLmBCJBIxb1Ag+dUyjubWGNocEx2MSaBuMqqaFOzPrGJKnA9iI+oLBLrZ0wfbM/B3tuaOfgGGNuemxcZCwqOjQknIq2FXWoWhzbmEMVEeWEvN2Hiy2NCmmOhgTAJ1k7E5pRSNVmBaT29Dm3IJB7OqSSmu58Hh3YyyX9HNxOy+/vg5W/Hl3hxDm3IJ1lIJY6M82HK6zNQm/gbH9Ba4ydifWYW/szURnvaGNuUSvtqfg7udBdN7GV9b+ZsNczMxd/cPICGvhrSyBkObcwnDw92pk6k4W2p8tploP0wCdRMhCALHC2rpHeBkaFMuoaxezv7MSmb39cdCYmZoc0wAt/X2QyoRs/pIgaFNuYTzVUVMRWRvbEwCdRNRVNtCVZOSXkYoUL+dKEYQYEZP0+zJWHCykTI5xotfk4toMrLuth72lng5WJJqmkHd0JgE6iYiq7IJgEgja48uCAK/JhfRy9/RVAzWyLizXwDNSg3bTpcZ2pRLCHazIbuy2dBmmOhATAJ1E1HZoAB0o09j4mxpIxnlTUzvZXwll252evo54mprwZ6MSkObcglBrjbkVZkE6kbGJFA3ERWNukrVbnYWBrbkYg5k6V5+46I8DGyJiX8jFosYFubG/sxKo4uYc7SS0ihXGV2ulon2wyRQNxFNCg1SMzGW5sYVhHA4u5pgNxvcjWxmZ0LH8HA36mQqThTWGdqUi7CSmqEVQGGqbn7DYhKomwgLiRilRmtUJWLUGi3H8moZEGzq9WSsDAnVVRwxtog58bkix6YJ1I2LSaBuIs7PnJQa4xlx5lQ106RQEx9ofJGFJnQ4WkvxcbQis7zR0KZcRH2LCqlEjKW56TV2o2K6szcRDla62naVjQoDW/I3meW6yMIwD+OKLDRxMaEetqSfu1fGQp1MiYOVuVG2izHRPpgE6iYizMMWgMwK4xkJZ58Lfe/mZmuQ88+bNw93d3e6d+9+2c8FQeCRRx4hJCSEmJgYkpOTO9lC4yDcw47siibURjT7zq1qxtfJytBmmOhATAJ1ExF6bpaSVmY8AlVaL8fFRmqwwI17772XrVu3XvHzLVu2kJmZSWZmJl999RUPPPBAJ1pnPPg6W6PUaKmRKQ1tCgBarcDZ0gYijCynz0T7YhKomwgHK3MCXaw5mmM8bQqqmhQGDXsfOnQozs5Xbor4+++/M3fuXEQiEf3796euro7S0tJOtNA4OO8ebmhRGdgSHamlDTTI1aaGljc4JoG6yRgT5cGh7Coa5MbxomlRarAx4pbuxcXF+Pn5Xfi3r68vxcWXb/Pw1VdfER8fT3x8PJWVxpfYej3YW+ruUb2RCNTOs+WIRDCom/H1NDPRfpgE6iZjfHdPVBqB7WfKDW0KoGs/LzUz3sfwckmgV1qUX7hwIYmJiSQmJuLm5tbRpnUqtucGEc0KjYEt0bn3fj9RQv8gF1Pu3A2O8b4ZTHQIPf2cCPOw5Zv9OUaRgS/CuCOwfH19KSwsvPDvoqIivL2Nr5dWR6M8lwxrDH26/kqrILeqmdv7+F17YxNdGsM/bSY6FbFYxMKh3Ugra2RHquFnURbmYuRqw4/Kr8SUKVNYuXIlgiBw5MgRHBwc8PLyMrRZnc75ag2GrkKi0Qos/SsTH0crJsfcfPfhZsN4nf8mrpt6mYrMikYyK5oorm2hpL6FOpnqwkL3wlVJRHrZ42orxdZCgoe9JcFuNnRzsyXWz/GCW6cjcbAyp6i2pcPPcyXmzJnDnj17qKqqwtfXl1deeQWVSvf9LF68mIkTJ7J582ZCQkKwtrbm+++/N5ithuR8uw1raccLlCAIZFc2k17WSE5lE7nVzTS0qGhSqDnyjwCf+SsSsbWQ4GZnQbCbDUGuNgS62ODtaIWZ2Lhn5iZah0mgbiDKG+TszajkSHY1yQW15FXLLnxmJhbhYWeBk40Ua6kZ5mYiVBpdqG5Pf0dK63X7ypSaC9v38HFgdKQ7U+N88HO27hCbXW0tqGxUIAiCQRIu16xZc9XPRSIRn332WSdZY7yU1OkGEZ4OHbPmo9EK7M2o4M9TZRzIqqS84e9kci8HSxytpRdFEA4IdqFOpqSoVsaedDnNyr9n4VbmZsT6OdA7wInh4e708ncyCVYXxSRQXZzsyiZ+P17M9tTyC/lNrrYW9PJ35LZ4PyI87QjzsLvsqPK1Tal8eyCXewYEMq2nD4IgUNGoIL2skYTcGg5mV/He9gze35HB5BhvHh0VSoh7+ybU+jlb06RQU92sxNXWuKqsm/ibkroW7Cwl2Fuat+txNVqBtccKWLY3m8KaFhytzRkU4sqQEFd6+DoQ5GqDtVRCi1LDbV8eoqFFxaZHBhPg8nffMEEQqGxUkFPVTG6VbuaVXFDLsr05fLY7G2cbKSPC3Rkd6c6wcDespabXXlfBdKe6IC1KDRuOF7MmoYCU4nrEIugT6MxzEyIYFuZGhKddq2Yjz02IIKW4nqd/OYm9lYSRER542FviYW/J0DA3niKcoloZq47ks+pwPttOl/H8xAjuHRTUbtdyXvCyKppMAmXEpJU1EtzO1T4qGuUsXJnEicI6evk78uz4CMZFe2L+r6hOhVrDoh+SOFPSwDdz4y8SJ9DNct3tLXG3t6T/P4oON8hV7MuoZGdqOTvPlrM+uQhbCwlT47yZ09ef7j4O7Xo9JtofUTtGchk+JOwGp6JBzrcHcll7rJD6FhURnnbc2tuXKbHebQ63rW9Rcdc3R0kva+StmT2YcYWmgZWNCv7z6yl2nq3gxUmRLBgSfD2XcoGKRjl9X/+L5ydGsHBot3Y5pjEQHx9PYmKioc1oF9QaLT1e3s7tffx4eUp0uxyzvkXFLZ8coKpJwRvTezA1zvuyg6raZiWLViWRkFfDOzNjmNXGyD21RktCXg2/JBXx56lSFGotvfwdeWB4CKMi3BGbXICdgd5fskmgugAVjXKW7clh9dF81FqB8dGe3DsokPgAp3ZZt6mXqVj8QxKHc6q5Pd6PFyZHXtaVo9EKPLg6iV1pFRx6blS7VYAY9f4e/JytWX5f33Y5njFwIwnUmZJ6Ji09wMez45ga59Mux3xj81m+PZDLTwv7Ex94+WoQ+zMreXrdKWqalbw3K5Ypse0T3l/fomJDchHfHMilqLaFcA87nhkfzsgId1Ph2Y5F7y/X5OIzYhRqDd8dyOPTXZnI1Vqm9/Th4ZEhl7g4rhcHa3NWzu/LBzsy+HJvNn+lVfDg8G7M7O17ocQN6AInZvf1Z9uZctLLGttNoAZ0c+HX5GJUGu0l7h0Thud8aaxe/u3XEuVEYR2RXnaXiJMgCJwqqmfpX5n8lVZBsJsNX88dSA/f9nPHOViZc++gIO7qH8CmU6V8/Fcm81ck0j/YmRcmRrXruUxcH6YZlJFyJKea59afIq9axuhId56fGNnuawCX42RhHW9sPsvR3BqkEjHDwtzo4eOAm50u2u6nY4XUypTsf2YELu20ZrQ5pZQHVyezdmH/i9YQuhLFdS1klDdSWienplnBOw/M4MWvf8PD3pJAFxvCPOyw6oQQ7Y5g1peHqZep2Pb40HY75rvb0vhsdzZT47wviFRWeSOHsqvJrGjCzlLCA8O7cd/AoA7/3lQaLWsSCvh4Zya1MiX3DgziybFhRl2Cq4ticvF1dWRKNe9sTWf5oTz8na15bVp3hoV1btkcQRA4XdzA+uQi9qRXkF8jQxBAJIIYHwf+b3LUFd0ybaFZoabP6zu5Jcabt2+NabfjdiSCIHCisI71yUXsOltBSb38os9LVzyG1z0fXfi3VCImPsCJ8d09md7TB7t2jobrKCoa5fR74y8eGRnK42PC2u24CrWG97dnsCahgEb53zlWsb6O3BLrzaQYr4tm751Bg1zFO1vT+OFIAT6OVrx3WywDunXNAZORYhKorkxWRSOLf0gmq6KJewcG8sz4cKMIiW1WqGmUq7G1lHRY8u7T606yOaWUYy+ONoprvhoHMqt4d1saJ4vqsZCIGRHuTv9gZ7r7OODtaIWLrZSB/fqx5+BhSurk5FY1k5hXw77MSjLKm7CWmnF3/wCWjAxp97Dt9ubLvdm8uSWN7Y8P7ZCmkhqtQHWTAgFdeoQx5Csl5tXw9C+nyKtuZsnwEB4bHYrE5HpuD0wC1ZUQBIH6FhXFdS2sOpzP2mO6mm8Dgl3oHeCEWiug0WpRawUEQVdmxlpqhpW5GdYWZrjZWuBmp/vjbmdpFHXS2kpCbg2zvjzMu7fGcFu8cdZYa1KoefWPM/ycWISPoxUPDO/G1Djvy86GrhQkcbKwju8P5vL7yRJcbKR8MCuOoZ08Q24tKo2WYe/sJsDFhjUL+xvanOuiTqakslFBdbOS6iYl1c0K6mUq1FoBrSCg0f79RywWIQgCX+/PvbD/t/fE083NFi9HSywkXdNVawSYBMoYUaq1ZJQ3klXRpCs9VN5ETlUzJXUtFyo3/BuxCCRiMRIz0YVRpUKlRXmFjqZiEfg7W9PNzZZgNxtC3e2I83ckxM22S4TQCoLA2A/3AbDtsaFGZ3NFg5y7v00gs6KRB4Z345FRoVd9UV0riu90cT1P/nySjIpGXpjYfmH77cnGkyU8suY438yNZ3SUh6HNaRX1MhXJhbVklTeRVdFEdqXuT63sym1CRCKQiEWIRbrfmkYrXKg9eDnc7Szwc7am27nfWYiHLdFe9qbK6tfGJFDGQHmDnITcGo4X1HGisJbTJQ0XqkFLxCICXW0IdtXVDFt+KA8AH0crvprbGzc7CxyszK/48lNrtLSoNDQp1FQ1KqlsklPZqKCotoWcymayK3Xid/58dpYSevk70TvAiSGhrsT6OnbKy79RruJsaSN51c3kVzdTWi+nuklJrUxJi1KDQq1FpdEiFomwkIhxspGSlF8L6IR2wZAgwjzsiPC0w9Fa2uH2Xo36FhXTPztIWYOcL+/uzZDQa894WhNm3qLU8OS6E2xOKeO1qdHcPSCwnSxuGxqtQH51MxnlTWSUN/LBjgwAevo70qLUoFRrL7y4LSRipBIxdpYSnKyl+DhZEeTa+fXwKhsVHMqu4lheDYl5taSXN3L+leZqKyXYzZZubrZ0c7PB3d4SVxspzrZSXGx0vzNzM9FlQ8s1WoEWlYaGFhU7Ust5aeMZACb28MRGKqGgRkZ2ZRNVTX93GPa0tyTG14FeAU4M6uZKlLe9UbgsjQiTQBkCuUrD4exq9mVWciCzisyKJgAszcX08HGgp78TMb4OhHvYEeBig1QiRqMVeHb9KX5JKmLxsG48Oz683XIwNFqBvOpmjhfUkZRfy/GCv3+4rrYWjIxwY2yUJ8PC3dotrLukroUDWVUczq7mZFEdOZXNFz4zE4vwtLfE1VZ6oRaghcQMiViEVtAtmNfKlFQ1Kkkvv7QdvYe9BeGe9sT5OtA/2IVeAU6dVlVbEATuX5nE3owKfpjfj36tjDJsbR6UWqNl0aok9mZU8vPiAe0ayn0t8qubOZJTTUJuLWdLG8iubLrszGFgNxdsLSRIJeILAyelRotcpaFJrqamWUlhrewib4CVuRk9fB3oH+TMsHA3Yn0d220dp7xBzobjxWw9XcbJojoEAWykZvQKcKJvoDO9A52I8rJv14FNZnkjd3+bQItKw8p5fYn1cwSgpllJZnkjKcX1nCqq51RR3YUamA5W5gzs5sLAEFcGh7gS5Nq+6SFdEJNAdRZNCjW70yrYeqaM3WkVyJQaLCRi+gY5MzjElYHdXInwsrusAAiCwPMbTrMmoYDHRofy2Oj2i466EnUyJXvSK9l5tpy96ZU0KtS42EiZGufDrD6+RHja633M/OpmNp0q5Y+TJf+oAyjVCbKPA919HAh2042mWyuEO1PLWbAykXsHBjI83I30skbSyxo5W9ZIelkDWkEXETewmwujIz0YF+3ZoS3jd6SWc//KRF6YGMn9Q1vvhtMnUbe+RcXEj/fjaG3OHw8N7rAZrlYrkJhfy86zutI/5wcRzjZSevg4EOZhS6iHHd4OVty/MpFob3vWLR7QqoHT+TqOuf+oh3e8sI6Uojq0gq4j79AwN2b29mVoqJveMwu5SsPOs+X8klTEvoxKtALE+DowOtKDEeHuRHrZdXggQ2GNjDu+OUKTXM0vDwyk2xXSPioa5RzOruZAZhUHs6ouRHiGutsysYcXk2K8OiTgpAtgEqiORKsVOJBVxc+JhWxPLUep1uJqK2VstCfjoj3pF+TcqpH9Rzsz+GhnJg8O78Yz4yM6wfKLUWm07MuoZH1yETtSy1FpBAaHuHL/0GCGhrpe9YUkCAIHs6r59kAOu9N1bc17BzgxPtqTIWGuhHu0rg7g1Vi0KpG9GZVsf2wY/i5/V1FvlKs4llfDgcxqdp4tp6BGhplYxLAwN2b08mFslGe7B4pM//wgdTIV2x8fqtdsU99KEhuOF/H4Tyf5/t4+jIhwb4upVySvqplfk4tYn1xMcV0L5mYi+ge7MCrCncGhrnRzs73onr288QwrDuexccng605arZepOJBVxd6MCnaeraCmWYmXgyW3xftxex8/fBytrrp/nUzJ8kN5LD+UR51MhZeDJTN7+TKzt69BZiR5Vc3cuuwQFhIzfn1wIB7XWHcSBIG8ahl70yvYfLqMY3k1CIKuBuXUWG9ui/frsArxRohJoDqC4roWfj5WyC9JRRTX6SouT431ZlKMN70D9Cvl/9vxYh776QS39vbl3VtjDF5apbZZydpjhXx/MJeKRgU9fBx4elw4Q/4lVBqtwMaTxSzbk0N6eSOuthbc3T+AW+N9r/mS0ZfS+hZGv7+XGF9HfljQ77LfryAIZJQ38duJYjYkF1PWIMfNzoK7+gVwV3//dkkizq9uZti7e9pUJ1BfgVKqtfR9YyfDw9z4aHZPfU29BEEQOJxdzTcHctmVVoFIBINDXLm1ty+jIj2umC6wJ72Ce78/xj0DAnhlavfrtuOfKNVa/jpbztpjhezLrMRMJGJaTx8eHxN2yTNU36Liiz3ZrDqcR7NSw+hId+4ZGMjAbq4GX9dJKarn9q8OE+Biw/oHBuiVFlHRIGfbmTI2nSrlaG4NYhGMCHdndl9/RoS73ejh7CaBak9OFdXx9f5cNqeUohV0s4zb+/gxJsqjTaGmaWUNTPvsIDE+jqy+v59RlfVRqrX8dryYj//KpLiuhdGR7rw6tTvejlYkF9Tyf7+d5kxJAxGediwYEswtsV4dGm67LrGQp385xcMjQ3hybPhVt9VoBfZlVrL8YB57MyqxMjfjnoGBLBwajLNN29chfj9RzKNrT7D1sSF6u0DbUovvwdVJpJY0sOfpEXrt928OZlXxzrZ0ThbW4Wor5a7+Aczu43/NkXplo4IJH+/DxcaC3x8a1KHrfEW1Mr49kMvqowWIgPmDg3h4ZCgWEjG/JBXx9tY0amVKJsd488DwbkR66e+C7kj2pFdw3/Jj3Nbbl3dujW3TMfKrm/npWCHrkoqobFTg62TFgsFBzOrjZ/S5gG3EJFDXiyAI7Mus4vPdWRzNrcHOQsId/fy5e0AAvk5tb9onV2mY+PF+mhRqNj0yGHc745zWK9QaVhzK48Mdmag0uhws0EUo/WdiBLfEeHdaCPgzv5zk58QivdxeWRWNfLIri40nS7A2N+OhkaHMHxzUJtff0r8y+WBHBhn/m6D3/m0RqPe2pfPZniyyXp/YplnCmZJ63th8loNZ1Xg7WPLwqFCm9/RpldAo1VrmfneU4wV1/PHw4E5bIymua+G9belsOF6MWATnHjfiA5x4ZWo00d7GWxfvfLmmpXN6XlchW5VGN7P8Zn8uifm1OFqbM3dAIPcMCGi3cmJGgqlY7PVwJKea97encyyvFm8HS16cFMntffzapSzN+9vTyalqZvWCfkYrTgAWEjMWDu1Gd28H7vjm6IX//3nRgIvWgzqDV6d2J6W4gUfWHOenRQOI8r72KDrE3Y6PZ/fkoREhvL01nbe3prEuqZBXp3RncKirXufXnhu8STpJkHUJorqcNn1QqDV88lcWX+zNxtHKnP9OjuLO/v6tnuEKgsBzv57iSE4NH8yK7dQFfB9HKz68PQ4LifhConqEp12rgzMMyWOjwziUXc0Lv6bQ08+xzV2nzc3EjO/uxfjuXiTm1fDlvhyW/pXJN/tzWDA4iPuHBneZ0ljtjfH4mAxIWlkDd397lNlfHaGgRsZr07qz5+kRLBjSPg9GUn4t3xzI5c5+/gwK0e8laQiS8mtZ8mMyDlbmTIrxwkIiZvZXh0kpqu9UOyzNzfj2nnhsLSXc830CBf9oYX8tQj3s+OaeeL67Nx61RuCub4/y4m8ptFwhMfpyOJ6rBVfZpLjGlu1DdZMCO0uJXi/m4wW1TF56gE93ZzGjpw+7nhzOvMFBeonTe9vT+TW5mCfGhF2xH1hHodZoefG3FNYeKyTC046e/o6klTXy/IbTqK6QlG4smJuJWTq7JwJcyJO6XuIDnfl6bjw7nxjKiAh3lu7KYti7e/j2QC4Kdeuf3RuFm1qg6mUqXt54hklLD5BSXM+LkyLZ+/QI7u4f0G7RYFqtwEsbT+Nlb8l/Jka2yzE7kmN5Ncz99iiO1lJ+XzKIz+7oxS+LByISiZj15WEOZ1d3qj3ejlasmNcXpVrL7K8Ok1vVfO2d/sHICA+2Pz6U+4cE8cORAm759ACpJQ2t2vf8usfJwjp9zW4TJ4vqiGll1JxGK/DetnRmfnGIZoWa5ff14d3bYnGwbv2AShAEPtiRwWe7s5nT14+HR4a01fQ2oVRrWfxDMj8cKWDR0GA2PTyY9YsH8uDwbqxJKGDJ6mTURi5Sfs7WPDIqhF1pFexOr2i344a42/HZHb3Y+NAgorzseW1TKqM/2Nuu5+gK3JQCJQgCPx0rYMT7e1h5OI87+vqz56nhLBgS3O4Lw3+cKuF0cQNPjw/vsEKr7UVeVTPzlh/Dw8GStQv7E3gujLeHrwO/LRmEr5MV9y1P6HSRCvOw48f7+yFXa7lt2WHSyy5N5r0aluZmvDApilXz+9LQomLGFwfZklJ6zf3i/B2xt5SwuRXbXi95Vc2cLm5gYLdrz7Ab5SoWrkzk091ZzOzly7bHhzI8XL/QdK1W4PU/z/LJrixm9/Hj9Wk9OtWlptUKPLXuJDvPlvPKlGj+MzESiZkYsVjEM+MjeOmWKLanlvP8hhTacZ28Q7h3YBBBrjb8b1Nqu8/6zkeyrprfF6mZmPu+P8aS1cmUN8ivvfMNwE0nUEW1Mu769ijPrk+hm5sNfzw8mNemde+QcjoqjZZ3t6UT5WXP1Nj26UTaUciUahatSsJMLGLFfX0vye9ws7Pgx/v74+tkzeIfkiisab27rT2I9nbg50X9EYvg1mWH2NOGkeSQUDf+fGQIUV72PLA6mc92Z1315WchMWN6Tx82nSrVy73YFr7an4NELGLmNVxshTUyZn5xiD0Zlbw2NZp3b4vV2w3dotTw4OpkvjmQy70DA3ljeo9Or334yh9n2HiyhGfHR3DPwMBLPr9vUBCPjAzh58Qi1iQUdqpt+iKViHlxUiTZlc2sSyzqkHMMCXVj86NDeGpsGDvPljPq/b2sOJSHVmvc4n293DQCJQgCPx4tYNyH+zhRUMfr07vz86IBHRoltDmllKLaFp4cG2Z0xU//zTtb08moaGTp7J5XXOx1s7Pg23vi0QoCD65ORq7qXJ94iLsdG5YMwtfJmnnLj/HVvmy9R9fnhXZqnDfvbkvnra1pVz3GA8NDMBOLeH1zaoeN5FNLGvjpWCF39rt6KHhWRRO3LjtEeYOClfP6tql2X+65RNNtqWX83+QoXrolqtOfzd+OF7PicD4LBgfxwPAr55c9NjqMwSGu/O/P1E4fEOnLyAh3Yn0d+HJfNpoOEg0LiS4qdfvjQ+np78hLG89wz/cJVNzAs6mbQqAa5CqW/JjM8xtSiPN3ZOtjQ7mzX0CHuzS+P5hHsKsNI/R0v3Q2WRWNrDqSzx19/a/Z+iHAxYYPZ8WRUlzPZ7uzOsnCv/FxtOKXxQMYF+3JG5vTuG/5MSob9QtisDQ348NZcdzdP4Av9+bw+p9nryg+ng6WPD4mjG1nyvkxoaA9LuEimhRqHlqTjIuNlEevUvIqv7qZ2V8dQaPVRVS2Jdjm9xPFTF66n6LaFr6+O575g4M6PVKuqknBSxvPEB/gxHMTrl5FRSwW8fatMWgFgfe3p3eShW1DJBLxwPBu5FfL2JFa3qHnCnCxYeW8vvxvWneO5dUw/uP97OzgcxqKG16gUorqmbz0ANvOlPOfCRGsmtevzeGg+nCysI4ThXXcOyjQ6GdPX+7NwdxMdM2E2POMjvJgSqw3X+3LobiupYOtuxQbCwmf39mLV6dGczi7mgkf7+PPU6V6zXDEYhGvTo3m3oGBfHMgl2V7c6647cIhwQwNc+O/v5/hr7Pt9yKQqzTcvyKR/GoZH82Ou2JScVWTgrnfJaDWalm7sB/hnvqFgVc2Knh4zXEeXXuCKG97Nj86xGDtM5b+lUmzQs1bM3u0qmqCj6MV9w4M4veTJR3uZr1eRkd64Glv2SEDmX8jEom4q38Amx4ejIe9JQtWJvLyxjNGH/moLze0QP2SVMTMLw6h0mj5aWF/Fg3r1mlisfFkCVIzMdN6Gvfak1yl4c+UUqbF+ehVdeGZ8eGotQIrz7UL6WxEIhFzBwTyx8OD8XSwZMmPydzz/THy9IjyE4lE/HdyFLfEevP21jQ2nSq57HZisYjP7+xFlJc9i39I4tfk619nqG1WMve7BA7nVPPebTFXDI6QqzTMW36M8gY5393bhxD31ouTWqNl9dF8Rr2/h22ny3hiTBhr7u/f7qWpWktts5K1CYXcFu+r13XcMzAAgPXt8L13JBIzMbf29uVAZiVVnZSaEOJux29LBnLfoECWH8rjnu8SqJMpr71jF+GGFCitVuDdbWk8te4k8YFO/PnIEOIDnTvt/IIgsCWllKFhrkbf0jsxrxaZUsP47p567efrZM2oCHfWJxcZdKE2zMOO35cM5uVbokjOr2X0B3t58beUVvvlxWIR794aQ3yAE0+vO0XmZdp9ANhaSPhhQT/6BDrzxM8neXPz2TbnpZwsrGP65wc5UVDHx7PjmN7zyoERb21J41RRPUtn92x1Kw5BEPjrbDkTl+7nhQ2nifSyZ8tjQ3hklGFbl29KKUWp0TJXz7UzLwcrYnwdOz16tC2M7+6JVoBdZzsvHNxCYsZLt0Tz7q0xJObVMu2zg2RV6BfpaqzccAIlV2l4eM3xc7kd/qyY1/e66rG1hdPFDZTUyxnf3atTz9sW0sp0OUGxvo567zsmyoOqJiXZlU3tbJV+mIlF3DsoiF1PDmNOX3/WJhQy9N3dvLzxTKsW1/f8tYNTyx6lpbGOWR9vvyT4Y8+ePTg4ODBsQB/OfL6ECEklX+7LYconB0nKr2m1nTKlmre3pjH984PIVVp+vL8fU+OuPMPekVrO8kN5zBsUxNjoaw8gNFqBradLmfLpQeavSESlEVh2Vy/WLux/xdYQncnRHF0JprbU1evp58jpks5NFG8L0d72+DhasT21rNPPfVu8Hz/e348mhZrpnx1iX0Zlp9vQ3hh3Yo6eNCvU3L8ykcM51bw4KdIgi8AAR3N1I70hepbWMQQNcjUAjnokeJ7nfCuGs2WNhBpBfxt3e0tem9adBUOC+HhnJj8cyWfl4TzGRXsyq48fQ0JcL5lBaDQalixZwo4dO8hpsWTBquO89PNh3r5z8EXbDRkyhE2bNl349+60Cp779RQzvzjMhO6eLBkRQnefy0eEylUa1iQU8NnubKqaFMyK9+WFSVE4WF35O69sVPD0LyeJ9rbn2QlXXxusaJSzLrGIH48WUFzXQqCLNW/N6MHM3r5GVZD4bGlDm9t3uNpKkZ3r6tveLVXaE5FIxMgId35JKkKt0Xb6jDU+0JnflgxiwYpE5q84xtLZPZnQw/gHylfihhGoBrmK+74/xonCOj6YFXtVt0lHk5Rfi6+T1TV7xRgD55fklBqt3tXJbc5VXO7scPNrEeBiwwe3x/H0+HBWHMrnp2MFbDldhpudBVNjvRkZ6U58gDNSiZiEhARCQkIIDg4mGAgz/4t1KQLzyxuvWpNuRIQ7u54czjf7c/lyXzZbTpfRJ9CJuQMCGR2pC0DIqWxi7bFC1iUWUitT0T/YmS/v7kXvgGu7m9/fnk6zQs3Hs3te9r7UNCvZkVrGxpMlHM6uRivAgGAXXpgUybhoT4O3pLgcMqWmzS5vpVqLWKR/nUJD0CfImVVH8kkra7zioKUj8XWy5qdFA5i3/BhLfkzm7Zkx3Bbv1+l2tAc3hEDVt6i4+9ujnC1t4NM5hh8xHC+oo19w5615XQ+h5xarM8ub9P4xnW/xLTWiUfo/8XKw4rkJETwxJoxdaRWsTy5ixeE8vjmQi7XUjIHdXLBrLsMpMAqNVsBMLGJGsIj30tS8szWNb+7pc+FYhw8fJjY2Fm9vb9577z2io6OxsZDw6OhQ7h0YyLqkQj7YcpqH82oBKC2uZ+T7ewEYH+3J3IEBDAh2adWM/kxJPT8lFjJ/UBAh7rYIgkBZg5yThXWcLKrnUHY1p861Og9wsWbJiBCmxvkQ4m54N97VsDI3o1mpbtO+mRVNeDlYdYl+ST3PtYM/WVRnEIECXbv5VfP7smhVEs+sP4VYJGJmb8MN2ttKlxeo86G6Z0sb+PLu3oyMMEz47D/tKWuQE2IEPv/W0NPfEZEItqeW6/1jOlGoexlHt6LKuCGRSsSM7+7J+O6eNCnUHM6uZm9GBXszKimskYLTaLq/tI1u7jbQaI0aCTvPVvDO1jSGhrlh6R3GvuNnsbC0YvvufUxZ8BRffbecmmYlBTUy8qtlZFY0IdNefgaamF9Dg1zF1tNlBLva4GZniYutFAcrc6QSMeZiMSqtFoVKS12Lkju+1lWRr2tRMX/5MVKK66k4l+slEYvo4evAY6PCGBnhTncfe6Ov+n2eMA87jhfUodUKekXTNinUHMisYmIXcVX5OFphLTUjq8Kwa7PWUglfz41n/opjPP3LSSzMxUyOaXtbEEPQpQVKrdHy8JrjHMuvYensngYXJ4DSel30mLeBQnn1xdvRihHh7qw8nMfd/QNws2td/xlBEFiTUEiAi7VRLMC3FlsLCWOiPBgT5YEgCPy28yBvf7uO8XcsJLeqmeOlwLkX/ud7svl8T/alBxn2EPNX6Ho9iUXg42RFkKstY6JC6envSC9/J0btdGDtE8NIyK0huaCWzIomfk0upknR+hnEn6dKCXCxZnCIK7F+jsT4OhDpZd+hjQQ7kvHdPdl6pow9GRV6/Va/3Z9Lo0LNHf38O9C69kMsFuHvbE1hTefnCP4bS3Mzvp4bz73fHePxn07gbC1lYBfoqHCeLitQgiDwf7+fZkeqrtjkLdfRMKw9Ka7VPZQ+Tl1DoAD+MyGCSZ8c4PGfTvDNPfGtegF+fzCPE4V1vDWj8+u4tRcikYhbRvTnyUVzuefNx/DxCaVPn/v5/YfVfHNaxR8nS3jn1hhQNGNmaYu5RExxXjZvvvYyG3/9BUdrKd6OVldctA9xtyXE3fbCi1UQBKqblVQ3KaluUlDfokKp0aLSCJibibCQiHl981kKa1rY/dRwAl2su8zsqDVM7OHF0r8yeWnjGWJ9HVvVjO9gVhWf7s5kUg8vYs+5zroCzjZSao0kH8laKuHre+K5bdkhFq1K4pcHBuqd7G0ojN+hewVWHclnTUIhS0Z0u2yxSUNR2aSbQbm3ciZiDIR62PG/ad05kFXF3d8evWpotkYr8PmeLF7dlMroSHdmddHF1/NIJBI+/fRTxo0bR2RkJLNmzSK2R3f8qhMBgZK6FiqO7+S/c8fxf3MnsOLNp1m79DXi/J0IdLXRK6JMJBLhamtBuKcdA0NcmdDDi6lxPtza25epcT4MDXOjuknJrHhfglxtbihxAp2r9d3bYqloUHDH10fJuUp6glarq5153/JjBLva8sb0Hp1o6fXjbCOlptk4BAp0a1Lf39cXawsz5i0/ZlS2XY0u2fI9Ma+G2V8dYXi4G1/dHW9UI/hfk4t44ueT7H16OAEuNoY2Ry9+P1HMCxtOo9RomRrrzbhoT7q522IjNaOiUcHR3Bp+OlZARnkTE3t48sGsuC7rbmoNty07RKNczdbHhuq9b1tavm87U8aiVUn8uKBfl3LD6Mv+zEoeXnOcZoWaaXE+jO/uSZiHHRIzEeUNChLzavglqYi0skYGhbiwdHbPLtf6/PkNKWw/U0bii2MMbcpFnCqq49YvDtMv2Jnl9/Xt7GjPG7/le0WjnAdXJ+PrZMX7s+KMSpy6OlPjfIgPdObz3Vn8mlzMuqRLS8tEetnz6R09mdTD64Yb4f+b8d29eG2TrpJ2Z9Rv3HW2AjsLCX2CukYEaFsZEurGtseG8smuTDZc4TmL9rbnw9tjmRrr0yV/44IgIDbC30eMryOvTo3muV9T+HBHBk+Na139TUPRpQRKqxV4bO0JGuVqVs7ve9VERxNtw8fRiten9+D/JkdxsrCOotoWZCoNLjZSYnwd8HXq+Be1sTD43CzmaG5NpwjUwewqBoW4GlVybUfhYW/J/6b14MVJUZworKOgWoZGEHCyNqe7T9d/ztQaAYmRCuvsvv4kF9Ty6e4shoa50deIB0RdSqBWJxRwKLuaN2f0IMLTOEObz79cFOquXVXY0tyMfsEu9DO0IQYk1N0We0sJSfm13NrBOSQ1zUqKalu4u39Ah57H2LA0N6N/sAv9g10MbUq70qLSYGHE7u+Xp0RzOKeaZ9efYvMjQ7CSGqetXWaoVlgj483NZxkS6srsPsa7MH++ekRZ/Y3bROxmQSwWEeFp3ymFN9NKdTURO7KBponOo6JR0eqUDUNgLZXw1owYcqua+XBnhqHNuSJdQqAEQeC5X3XZ0G/NjDHqtQ+vcx1Ry27gLpc3E4Gu1uR1Qh+i8321/Jy7TnqCiStT3iA3+kjeQSGuzOnrzzf7czheUGtocy5LlxCoLafLOJhVzXMTIgzWy6a1eNhbYiYWkV/d+r5EJowXNzsLapqVHdbu/TznZ9xdoX6jiasjV2korJER7Gr8Ubz/mRiBh70lz/xyyiibHRq9QCnVWt7akkaEpx1z+hp/JrlUIibC046ThcbfGsDEtXGwMkejFfSqANEWmpRqpBLxDR22f7OQVdGEVoBwI10n/yf2lua8MiWazIom1iUaX0NIoxeoVUfyKaiR8Z+JkUZZoflyxPo5crKozqCN/Ey0DxKx7iei7ejBpdA1KnWbuDYni+oA469ReZ4xUR709Hfkk12ZRteZwKgFqkGuYulfmQwJdWVYmJuhzWk1cX6ONMrV5FQZtlikietHfU6ZxB38SzENZW4cjuTU4GFvQYBL1wiVF4lEPDU2nNJ6OWsTCgxtzkUYtUD9fKyQ+hYVTxt5Mtm/GXAuZHZ3WtfvaHmzUytTIRGLLvS+6igcrMyRq7RGN4I1oR8arcDBrKpWt1YxFgZ2c6F/sDOf7s6mRWk8z6DRCpRao+X7g3n0DXQmpg3tyA2Jn7M10d72bD3T+W2fTbQvFQ26cOGOrmZwPiS5okHRoecx0bEk5NZQ06xkbLSnoU3RC5FIxJNjw6lqUrD6aL6hzbmA0QrU9tRyiutamDc4yNCmtInx0Z4k5dea8qG6OIW1sgupAx3J+ejUwtqOD2k30XFsTinFQiJmeHjXWZI4T59AZ/oEOrH6aEGHR622FqMVqG8P5OLvbM2YKMP3eGoL59t/rD1mXD5dE61HqxVILWnolOTZKC/dgvrpYlP0Z1dFrtLw+4lixnf3xLqDXcIdxew+/uRWNZOQW2NoUwAjLXWUWd5IUn4tL07qOpF7/ybQ1Ybh4W6sPlrAg8ND9GrLYAzUyZTkVDWTV9VMWYOcykYFFY0KKhsV1MtUtKg0tKg0yJUa5GoNIpEIiViEmVj3t7VUgoOVOQ5W5jham+NiK8XH0RpfJyt8nKwIcLY2+grVudXNNCnUdPfp+GgsJxspPo5WnCoyfoFSqrUU1sooqJZRUCOjpL6FygYFlU0KGuRqmuQqGuVqmhVqNIKAVtCJvZlY1/PK0twMK6kZjtZSnK3NcbKR4mZrceHZ8HOyJsBFv1YmxsDGkyU0yNXcbsSVbq7FxB5evLzxDD8dK6SfEZSfMkqB2pxShkgEU4ykCWFbuWdgIPd9f4wtp0uZGudjaHMui1qjJauyiZSiek4X13OmpIHsyiZqZaqLtrO1kOBmZ4GbrS46yVpqhpVUgpW5GRbmYgQBNFotaq2ARivQrNBQ36KkvkVFVkUTh7J1Dfr+iautBZFedkR42hHpZU/vACf8nY2nSd+edF2QS2fViesX5MxfaRWoNFqjKRgrV2k4W9rA6ZIGThfVk1JcT0Z5I+p/pFBIzcS42VngameBo5U5vk5W2FlIsJZKMDcTIRKJEItAIwgoVFoUag3NCg11LSqqmpRklDdR2ahA+Y9EUYlYRKCrDWEetkR42hPn50isn6PRFojWagW+3JtNpJf9hSCproiV1Iwpcd6sTy7ipSnRBv++jVKgtpwuJT7ACfcunlU/LNSNbm42fLIri0k9vJAYwUtHoxU4W9rA4exqDudUcyy3hsZzSajWUjOivOwZ392LYFcbglxtCHKzwcvBsl1cFo1yFcV1LRTXtpBb1UxaWSPpZY2sPJx/obiuq60FfQKdGBjiyvAwt06pIn4l/jpbTqi7baf19Rob7cGvx4s5llfDwG6G6Qel1mg5UVjH3oxK9mVUcrqkAc05MTpfafz+8GBC3W3xd7bG38UaN1uL6x5UaLUCVU0KiupaKKiWkVnRSEZ5E6klDWw5Xcb5JZEQd1v6BjkzJMSVgd1ccbA2DsHanlpOdmUzH8+OM5oBVluZFe/H6qMF7Egt7/AiydfC6AQqp7KJtLJG/js5ytCmXDdisYinx4Wz+Idk1iUVGawSRotSw/7MSnaklrMrrYLqc900g11tmBzrTZ9AJ2J8HQhyte1Ql6qdpTkRnuaXVKLXaAUyKxpJzKslKb+WhNwatpzWRUAGu9kwNsqTyTFeRHvbd9qPv7pJQUJuDQuGBHfK+QCGhrlhIRGz7XRZpwpUvUzFttQy9qRXsD+zika5GrEIevo7sXhYMD18HOnuY4+Po1WHff9isQh3e0vc7S3p5e900WeNchWniuo5XlBLckEdG0+U8OPRAsQiXX+jMVEejO/uSTc32w6x7VqoNFre2ZZGNzcbJvXwMogN7UkPHwdcbaUcyKw0CdS/2XamHIDx3btWmOaVGBftSXyAEx/syGBKrDc2Fp3zlas0WvZnVvJrcjE7z5YjV2mxs5QwMsKdEeHu9A92wbMTotNag9m5quERnvbc1T8AQRDIqWpmb3olu9Mr+GZ/Dsv2ZhPkasMtMV7c2tsP/w5Ogvw5sQi1VmBmr85zzVpLJYyJ0s2inhkf0aHPilKtZVdaOesSi9iXWYlKI+Bpb8nE7l4MC3djkBHNTuwszRkU4sqgc/25VBotJwvr2J9Zxd6MSt7dls6729IJdbdlSqw3M3r7dmrNzjUJBeRUNvPN3Hij8JJcL2KxiMEhrhzIqkKrFQzaMNLoWr7f+30CxbUt7HhiWHsczihIyq9l5heHeGB4N54dH9Gh58qvbuaHI/lsOF5MVZMSR2tzJsd4MaG7F32DnI1mbUMfapuVbD1Txh8nSziSU40AjAh35+4BAQwLdWv3H5Bao2XE+3vwdrDip0UD2nSMtrR8B0guqGXG54d4ZUo09wwMbNO5r0Z5g5zlh/L4+Vgh1c1KPOwtmBLrzeQYb2J8Hbqke6qsXs721DL+PFXK0dwaRCJd4umseD8m9vDq0Ge+olHOmA/2Eellx5r7+3fJ7+9yrE8q4sl1J/nzkcHtGcXatVu+a7UCxwvqGN/FktyuRe8AJ27r7cuXe7MZHelB7wCna++kB4IgsC+zihWH8tidXoFYJGJMpAczevkwPNy9y0VD/RsnGylz+vozp68/ZfVyfkwo4MejBdz3/TECXKy5d2Agc/r6t1uh1Q3HiymsaeGFiZ3vZu7l70RPf0e+P5jLnf38221EnlXRxNf7cthwvBi1VsuYKA9m9/FnaJhbl42UPY+ngyVzBwQyd0AghTUyfk0u5pfkQh5de4I3N6dx94AA7ujrj5ONtN3P/fLGM7QoNfxvWo8bRpwAhoTqZqv7M6sM2qPMqGZQ2ZVNjHp/L2/P7MHtfYy/crk+NMpVjP9oP+ZmIjY/OqRdgg60WoHtqeV8ujuT08UNuNpacEc/f+7o62807ruOQqnWsvVMGSsO5ZGUX4uHvQVLRoRwex8/LCRtFyqFWsPI9/bibCNl40OD2vzSaesMCmDbmTIWrUri9endubPf9XXYPV1cz8d/ZbIjtRxLczGz4v1YMDi4w12khkarFdiTUcF3B/I4kFWFpbmY2+P9eHBESLu1NPnjZAkPrznO0+PCWTIipF2OaUyMen8PwW62fD03vr0O2bVnUMn5uqZZ/14kvRGwszTn/VmxzPn6CG9sPsv/pvVo87EEQWBPeiVvbUkjvbyRQBdr3p7Zg2k9fa7r5dyVkErETIn1ZkqsN4eyq/hwRwb//f0My/Zk89S4cKb39GmTuKw4lEdxXQuvT+9usBHx2CgP+gY588H2DG6J9cbeUv+1oKJaGe9vz2DD8WIcrMx5dFQocwcEGH3uWXshFosYGeHByAgP0ssa+fZADquPFrDmWCF39vPngeHdcLdru1DlVTXzn19T6OXvyMKhnRdI05mEediRXtbx3aSvhlH5frIqm5CaiQ0WjdPR9A92YcHgIH44UsCG423rvXKmpJ67vj3KfcuPoVBr+Hh2HDufGMbtffxvGnH6NwO7ufLzogH8ML8fbvaWPPHzSW7/6ggZ5fr9uPKrm/lgRwajI90NWj1fJBLx38lR1MiUvLctXa99lWotn+3OYtT7e9mcUsoDw7ux75kRPD4m7KYRp38T7mnHO7fGsuvJ4UyN9Wbl4XxGvLuHz3Zntak4b4tSw5IfkzETi/jkjl5dcl23NYS425JfI0OpNlwjQ6OaQZXUyfFytDRo1EhH88z4CE4V1fPs+hSCXW2J9XNs1X4NchVvb0njx4QCHK3MefmWKO7oF9Dl15faC5FIxOBQVwZ2c+GnxELe2pLGxI/3s2BIMI+NDr3m+pRWK/CfX1MwF4t5bZrhZk/n6e7jwH0Dg/juYC4jI9wZHu5+zX2SC2p55pdTZFU0MaG7J/83OQpvI+9A3Zn4u1jz7m2xPDgihDc3n+XdbemsSSjglSnRjIpsXUk1rVbgiZ9PkFrawLf3xBt9h+/roZubLRqtQF51M2EedgaxwajebiV1LXg73Lg3HMDcTMznd/bC3c6CecuPkVN57Z5R28+UMeaDvaxJKGDeoCD2PD2CewcFmcTpMojFIub09WfXk8OY1tOHZXuzmfrpQTKvMZv6Ym82h7Kr+c/ESLyM5Bl8Znw4YR62PP3LKWrO5a5dDqVay3vb0rn1i0O0KDV8f28fvrirt0mcrkCQqw1fzY1n9YJ+WJmbMX9FIg+vOU5V09UryQuCwNtb09hyuowXJkYyMqJr1gltLSHuOk9WVoXh+toZ1RuupK7lpvhRudhasHJeXwDu/jbhihXP62UqlvyYzMJVSThZS9nw4CD+b3KUwcuPdAVcbC1477ZYVszrS1WTgls+PcBPxy5fpXl/ZiXvb09nSqw3c/oaTx01S3MzPrq9J/UyFQ+vSUaludTVUlrfwu1fHebT3VnM6OXL1seGMCLi2rMtEzAoxJU/HxnC46PD2Hq6lNEf7GXbVVrkfLgjgy/35XBXf3/md9EuC/pwPtDqWsLdkRiNQKk1Wsob5Pg43tjRZ+cJdrNl+X19qW9Rccc3Ryitb7no8xOFdUxcup/tZ8p4ckwYfzw8uNXuQBN/MyzMjS2PDqF3gBPPrk/hiZ9PXrTukF3ZxOIVCQj1pfz58p28/fbblxxDEAQeeeQRQkJCiImJITk5udPsj/K25/Xp3TmYVc0rf5y56LPD2dVMXnqAjLJGPrujF+/dFotdGwIqbmakEjGPjg5l8yND8HOyZtGqJJ7fkHJJ076PdmawdFcWt8f78eoUw7uAOwPbc4niTedKoRkCoxEouVqLVuCm+oH18HXg+/v6UNGg4LZlhymoliEIAt8eyOW2ZYcAWLd4IA+PCr1hF2I7A3d7S1bO68cTY8LYcLyYud8mUCdTUlrfwt3fHqW5qYGV9w/mbMoJ1qxZQ2pq6kX7b9myhczMTDIzM/nqq6944IEHOtX+2+L9WDQ0mB+OFPDJX5kA/Ha8mLnfHcXR2pzfHxrMpJiuX2LHkIR62LH+gYEsGhbMj0cLmPnFIQprdL/HT/7K5KOdmdza25c3Z/S4odfI/4mFRIxELKJJbjiBMpogCY1G53rp6kmD+tIn0Jkf7+/H3O8SmPrZAdzsLMgob2J0pAfv3RaDo3X7JxfejJiJRTwyKpQgVxue/Pkkg9/ejVqrRSRoCcj7kyE95wAwe/Zsfv/9d6Ki/k7S/f3335k7dy4ikYj+/ftTV1dHaWkpXl6dJwrPjo+gslHB+zsy+P5QHjXNSvoHO/Pl3fEml287IZWI+c+ESPoHu/DImuNM/uQAXg6WpJU1MqOXD2/PjLlpxAl0gUdqrUB+teGaaBrNsFyt1fnXJWY3zwNwnhhfR766O55amYqM8ibi/Bz5em5vkzh1ALfEevPGjB40KdTIVVqm+ykJdf3brezr60txcfFF+xQXF+Pn53fVbToasVjEO7fGAFwImFgxr69JnDqAEeHurLm/P/UtKtLKGnGyNue9W2NvusHzef5MKTXYudutksT48eOFs2fP4ubWtvwRtUbgbFkDPo5WOHdASZLWUllZ2eZraCsqjZbcquYLLScAPOwtcbdrW96KIa6hvemoa5CrNORWNV/oZyQRgaWqnqAAXeWS6upqmpub8ff/u5JJZmYmXl5e2NrqopoyMjLw9fXF2vriagyVlZVUVVUBoFAoiIuLa1fbKxoVlDf8HVDjbCPF29FK//T8VnKzPkcKtZb86ot/j572lri18fd4PRj6HqQU12NlbnYhoq8tnL+GpKSkbYIgjNdrZ0EQ2uuP0Lt3b6Gt1DYrhIBnNwnf7s9p8zHag+u5hrZQWtciDHl7l9D9v1uFg1mVgkyhFh5ZkywEPLtJuOubI0Jlo1zvY3b2NXQEHXENW1JKhMj/2yL0+d8OIa20QTiWWy2EPb9JCH1khVAnUwqCIAhvvPGG8MYbb1y038KFC4Uff/zxwr/DwsKEkpKSq57L2tq6XW3//USxEPDsJuGRNcmCSq0R3tx8Vgh4dpNw3/cJF2xvb26250ir1QrrEguF6P9uFXq+ul04mFkpKFQa4eEfdb/Hj3dmdKCll8eQ90Cr1Qohz/8pvLXl7HUd5x/XoLeuGI2Lz87SHJEI6v7VdfVGpqJBzh1fH6GmWcnK+X0Z2M0VK6kZH90ex5szenA0t4YJH+9nZ2q5oU3t0qg1ujyhxT8kE+Zhxx8PDybc0474QGe+nhuP0sKRxd8fQi5XsHbtWqZMmXLR/lOmTGHlypUIgsCRI0dwcHDo1PWnE4V1PL3uJH0DnXnn1hgkZmKemxDBa1Oj2ZdRyZRPD3CmxPhbxRszNc1KHlydzFPrThLlZc/GhwYxMMQVqUTMh7fHMaOXDx/syGDpuSCVmwGFWotKI1yI5jMERhMkYSYWYW9pTr3sygmJNxK1zUru+OYoZQ1yVs7rS89/1B8UiXTJpnF+jjz+0wkWrExkek8fXrolyrQupSf51c089tMJjhfU6UKEp0VfVBJqaLgHs0LN+Dm7icjbnmTBrFlER0ezbNkyABYvXszEiRPZvHkzISEhWFtb8/3333ea/WX1cu5fmYibnQVf3NXrItvvHhBIpJc9S35MZsbnh3hmfAT3Dgy8addK2squtHKeXZ9CnUzJfyZEsGBI8EXfoZlYxLu3xgLwwY4MnGyk3N3/+or4dgXOh5fbW94gArVw4cLr2t/FRkqlAZPC4PqvoTUo1BoWrkqkoEbGivv6Eh/ofNntIr3s2fjQYD7bncVnu7PYn1nJM+MiuLW371WjiTrjGjqa670GrVZgdUIBb20+i1gsYumcnkyJ9b7stm8vmIhm3SnWM4Ghs3QJ1IsXL77wuUgk4rPPPtPr/K6u198RV6sVeOyn48gUan6YP+iytfTiA53585EhPPPLKV7blMrW06W8c2ssQa7X36b+Rn+OCqplvPZnKjtSywn3sGPFfX2J8ra/7LZmYhHvzIyhXqbipd9P425nwbhOaAtkyHtQd26yYH+dgTjXcw1G1W7j3u8TqGhQsPnRIe1hj1EiCAJPrTvF+uSiq740/82Zknr+77fTJBfUEevrwH9viW73vlI3CmdK6nlhw2lOFNYxKMSFd26NvWbNNLlKw8SP96PUaNn22NDr7mZ7Pe02zvPN/hz+9+dZ3rk1hlnxV69wIQgCvyYX88ofZ1CotTw0IoT7hwa3W4+sG4kWpYYv9mSxbF8OErGIh0eGMm9wYKuKLcuUauZ8fZTM8kY2PDiIcE/D1KjrDLaeLmXxD8lsfGgQMb6O7XFIvaf2RrMGBboaWXnVzZctR3OjsPZYIeuTi3hkVGirxQkg2tuB9Q8M5KPb4yitlzPzi0MsWJFIaklDB1rbtSitb+GpdSeZ/MkBCmtkfHh7LD/M79eqgp6W5ma8NTOGotoW3tuuXwXxjqC4roX3t2cwOtKD23r7XnN7kUjEzN6+7HhiGCMj3Hl/Rwaj3t/LplMlN/TvSR/kKg3f7M9hyDu7WboriwndPdn15HAeGN6t1Z0ArKUSvrq7NzYWEhauSqRBfuOumaeXNSEScV0RfNfLdQmUSCR6VyQSpYlEolPTp0+nrq7usttt3bqV8PBwQkJCeOutt654vGBXG2RKDaVXqE3XEaxbt47o6GjEYvFVR7yBgYH06NGDuLg44uPb1sArtaSBlzaeYWiYG4+NCtV7f5FIxLSePux6ajhPjQ3jaG41E5fuZ8pbvxMxcNw1r6G196GzqampYcyYMYSGhjJmzBhqa2svu92V7kFFo5w3N59l+Lt72HiihPuHBLPryeFM7+mrV0mavkHO3N0/gOWH8jhd3Lqgg2t9p0IbyyS99kcqAgIvT4nS6xo87C354q7erLm/P3aWEh768TgTlx5gS0opWu3lhepa17Bnzx4cHByIi4sjLi6OV199tdX2dAbz5s3D3d2d7t27X/ZzmULN5CfeI+Kpn/jfn2fxshb4ZfEAPp7ds02NPT3sLVl2Vy+Kalt4ccPpdhkAXOsaDHEPMsob8Xe2blVz1cLCQkaMGEFkZCTR0dF8/PHHl2wj0rFUJBJliUSiUyKRqNc1D9yW0L/zf4CxgEQQBJ555hnhmWeeuSTEUK1WC8HBwUJ2dragUCiEmJgY4cyZM5cNR0zOrxECnt0kbD519RDe9iQ1NVVIS0sThg0bJhw7duyK2wUEBAiVlZVtPo9cpRbGfbhXiP/fDqG6SdHm4/yTumal8O7WNCHyxT+FgGc3CWEPfC58/vt+QaXWXLKtPvehs3n66aeFN998UxAEQXjzzTcv+xwJwqX3IL+qWXhxQ4oQ+sJmIei5TcJja48LBdXN12VLnUwp9HhpqzB/+ZWfhfNc7Ts9H1r7559/CuPHjxe0Wq1w+PBhoW/fvtc8btK538H1hjWrNVphfVKhMOLd3ULAs5uEMR/sEX47XiQoVH8/H615Lnbv3i1MmjTpumzpSPbu3SskJSUJ0dHRF/1/YU2z8MbmVCHyhU1CwLObhNu/PCR898e+Vt2D1rB0Z4YQ8OwmYX1S4XUf60rXcB5D3INR7+8RFqy49u9AEAShpKRESEpKEgRBEBoaGoTQ0NBLniNgIrAFnauvP3BU6Mgwc0EQtguCoAbo378/RUWXNuFLSEggJCSE4OBgpFLphVIylyPa2wELiZik/MuPoDuCyMhIwsPDO/w8n+3KIq2skbdn9mi3RGQHa3OeGhfO0RfG8OKkSNQWjrx9qJ7Bb+/m/e3pFNb8XaJEn/vQ2fz+++/cc889ANxzzz389ttvV9xWoxXYkVrOPd8lMOy93aw9VsCMnj789eRwPrw9Dj/n62tl7mBlzoIhwew8W05K0dVnUa35Tq9UJulqfLgjAxcb6XVXzDYTi5jRS+f2+3h2HFoBHl17goFv/cXbW9MorJEZ9XPRWoYOHYqzsy7QSKnWsv1MGQtXJjL0nd18sz8XO1kJC7s1s3bhAO6bPKRV96A1PDgihN4BTry2KfWq7VD0vQZjoEWpS2gPb2UfKC8vL3r10k2I7OzsiIyMvFy1lanAynN6dQRwFIlEV83XaLc1qO+++44JEyZc8v/6lImRSsTE+jqSVNB5AtVaRCIRY8eOpXfv3nz11Vd67ZtT2cSyvTlM7+nTIT1k7Cx1L1XfE1/z9AAHIrzs+HR3FkPf3c3srw6z6nAeZ/MMX67nSpSXl1/IK/Ly8qKiouKizwVB0Lnc4mbQ/40d3L8ykaTsMh4ZGcr+Z0by1syYdolaO899gwJxsDLnk11Xz3lpzbOtb5mkjPJG9mdWMW9w0HUHapzHTCxiapwP2x8byvL7+tDT34kv92Yz9N3dvLy7ErOQQRcitq5k3+HDh4mNjWXChAmcOXPmks8NiUYrkFIqQ9F9Kv3e2MnCVUkkF9SycKium7Bbxu8Mjfx7vbe9nn0zsYg3Z/SgUa7mjc1nr/t416Iz70FCXg0arUCfIP1FMy8vj+PHj9OvX79/f+QDFP7j30Xn/u+KXPMXIBKJdgKXi6d8QRCE389t88K0adO48847L9lIuIx/9mo+9T5BTny5N4d6mQoH6/apMzZ69GjKyi7t8/L6668zderUVh3j4MGDeHt7U1FRwZgxY4iIiGDo0KGt2ve1TalYSMQ8PzFSL7v/SWuuQSRo6edjyZKp8RTXtfBLYhEbTxbzf7+fQYQlDg6D+WJPNkPDXNEKV78P7c3V7L8cSrWWxLwadqVV8FdaBblVzUiiRjM83I0xIXa8vmQOvcd9jKdDWLvbamdpzh39/PlybzZl9fIrrlO05tnW9/lfcSgPC4mYO/r6X3GbtiIWixgeruvOW1LXwtpjhazan06tXW/i/7eTAd1ccG6yQC6++Hp79epFfn4+tra2bN68mWnTppGZadiE1foWFfsyKtmVVsGe9ApqZSrw68OgEFdm9vJlcKjrhQ4A+t4DfQjzsGPh0GA+35PNHf386eXfMZG1nX0PDmRWIjUT0/cKKTBXoqmpiZkzZ/LRRx9hb39JyP7lvvSrLuBdU6AEQRh9tc9FItE9wOTVq1df9qb7+vpSWPi3aBYVFeHtfeXotTFRnny2O5udZ8uZ2Yropdawc+fO6z7GeZvd3d2ZPn06CQkJrRKooznV7E6v5D8TIq6rlpe+1+DjaMWjo0N5ZFQIGeVNfLklgU0nRLy9NY23t4KVyA4fx36sPppPTz8nwj3tOjTB82r2e3h4UFhUQpXWir9O5eM05Tl6vbaDJoUaqZmYfsHOLBwazITunhcSlc9Om9rqe9AW5vTx54s92axPLmLJiJDLbtOaZ1uf51+p1rLpVCkTunvi1MH1KL0drXhiTBj9bar4zzufM3Hxi2xOKWV/tQ1Yj2Dke3sYGOLCwG6u9PR3xNNGJ1oTJ07kwQcfpKqqql1yvVpLvUxFckEtCXk1HMut4XhhHRqtgJO1OcPD3enhIuL9p+bz6buXBgnp+w7SlyUjQvg5sZC3t6SxdmH/Dhn4/fNl3xn3YF9GFb0DnLCStj5NQaVSMXPmTO68805mzJhxuU2KgH/mS/gCJVc75nX5EEQi0XjgWWCYtbV1xeW26dOnD5mZmeTm5uLj48PatWv58ccfr3jMWF8HvB0s2XK6rN0E6nppbm5Gq9ViZ2dHc3Mz27dv57///W+r9n1/ewYe9hbcMzCwY428AiKRiHBPO965exi/vRbGuo1byZFJefGTH6jq1psXNpwGwEZqRpS3PeGedoR72BHmYUeAiw3udhbt2mJAqxUobZCTX9VMdmUTqaUNWE97meGfJqE553G29QzmllhvRka4M7CbCzYWEt090CgAqd73oC34u1gT5+fIltOlVxSo1jzbU6ZM4dNPP2X27NkcPXr0qmWSDmZVUd+i4hY90g+ul759+1J46i5mhVvw2IiB9B41hdmPvkROszkbkov54UgBoCtMG+Vlj5OoGa1/byqU5kjlKuzbuX9bo1xFXpWMnKomciqbyapoIqW4noJz66kSsYjuPg4sGhrMqEh34vycMBOLyMvL4wP15aN/9bkHbcHGQsLDI0N5aeMZDmZVMzi0/UWjrKwMDw8PRCIRCQkJaLVaXFxc2v08oGvimV7eyP9Njrr2xucQBIH58+cTGRnJE088caXNNgIPiUSitUA/oF4QhKsuBl6vk/tTwALYERcXR//+/Vm2bBklJSUsWLCAzZs3I5FI+PTTTxk3bhwajYZ58+YRHR19xQOKRCLGdfdk9dECmhTqDq8DtWHDBh5++GEqKyuZNGkScXFxbNu27aJrKC8vZ/r06QCo1WruuOMOxo+/dlHepPwaEvJqeOmWqA5NmGzNNZy/D3fOmHzhPjz//HgKa1o4XlhLcn4tqaUN/H6ihMZ/NCiTSsT4OlrhYW+Jq50FrrZSHK2k2FiYYS2VYC01uyBgInSV2WVKDS1KDTKlhroWJZWNCqqaFFQ0KiiqbUH5jyrRjtbmhAb4kpGwi6a8FHwtFGxYswJnZ2dKSkq4bfqU67oH18O4aE/e3ppGZaPisrPfKz3by5Yto7KyEkCvMkm70yuwlpoxJLTzqldf7hpeuG0gy5Yto7cXDJh0O5/9uJG9J7M5XOyDxt4T8cB5TFx6ANB1XfVysMTL0QpvB0scrM2xOfdcnH8+zMQiVBrtuT8CKo0WhVpLTbOSqiYF1U1KqpsVlDcoqGz8u5KMSAS+TlZ093bg9j5+9PR3pKffpaP6OXPmsGfPHqqqqvD19eWVV15BpdLlJ3VWqarZff34bHcWX+7LbpNAXesafvnlF7744gskEglWVlasXbu2w1z0f54qRSSCST1aL+IHDx5k1apVF9JAAN544w0KCnQDnHOVWTaji+TLAmTAfdc6rlFVkjhPQm4Ns748zAezYpnRyzhmUW1hyY/JHMis4tBzI9ttwbujEQSB0no5GeWNFNa2UFQjo6BGdkFkqpqUerWAtrWQ4Gorxc3OAldbC/ydrQlwsSHQxZpAVxu8HCyNtn12Yl4Nty47zJd399a7rE1bKkmM+3Af7vYWrJp/yeKy0aDSaMmpbCa9vJHSuhZK6+WU1LVQ1iCnpE5Og1x10QDkakglYtxsdYMeF1sL3GwtCHS1IcjVhmA3G/ydrbtUJYwv9mTz9tY0tj42hAjPy5dMMnYEQWDU+3txtbPg50UD2vvwev/QjfKtGR/gRLCbDSsP53dZgaqXqdhxppw7+vl3GXEC3QzW29EK76tUX1BrtLSodDOkZoUaXf7n+Y7I4nOjZzOszM2QdOFW9d19HDA3E5FcUNvhddfqZSrSyxu5Jda4W7ebm4l1buCrlPhRa7TIVBpkCg3NSjWCICARizGXiDEXizA3EyOV6J4TYx2ctIXb+/jx4Y4M1iYU8vKUK3uJjJlD2dXkVDXz8KjLu7U7G6N8c4rFIub2D+DlP1I5WVhHrJ+joU3Sm00pJSg1WmZ2UYG9GhIzMXZmYuzaef3B2LA0NyPK24FThR3fyiKzohHQ5QJ2dSRmYuzNxO2+PmXsONtIGdfdkw3Hi3lhUuSFKMKuxA9H8nGyNmdCd+MYKBntNzizty82UjNWHM4ztCltYkNyMWEetnT36ZpTfRM6/J2tKa1v6fDz5FY1A7RrPpeJzueWGC/qW1Qcyak2tCl6k1/dzLYzZczq42c0rlWjFSg7S3Nui/fj9xMlF368XYU6mZKkglom9vC6oVwYNyMedhaUNcg7vOBqVZMuUdbdvvPbiptoP4aGuWFlbsa2M5fm/Bk7y/bmIBGLmT/o+iqYtCdGK1AAD47ohtRMzAc7Mgxtil4czq5GEGBwSOfliZjoGFztLJCrdJGJHUmdTHluXcYove4mWomluRn9gp1JyK0xtCl6UVgjY31SEbfG++Jur38B3Y7CqAXK3c6SeYMD+eNkSZdqaX0wuwobqVmXXDszcTGd1ZxWrRWQdsE1CxOX0svficyKpi7ViuOdbemIxfDwSOMIjjiP0f8iFg7thoOVOe9uM3yPntZyuriBGF/HLrlIauJizneo6AxPrdbUt+mGoKe/I4IAJwvrDG1KqzheUMsfJ3Vtarwcrt07rTMx+jeog5U5S0Z0Y096JTtSyw1tzjURBIHsiiaDNvky0X60KDWIRHT4YMPWQoJMqUFzhZ5NJroOcX6OiERwoqDO0KZcE41W4LVNqbjaWrBoWDdDm3MJRi9QAPcODCLC047/++00jUY+ba5oVNCoUJsE6gahvEGOi41FhwuUi62u9l51k+IaW5owduwszfGwsyT/H+1ujJWVh/NILqjj+YkRHV61py10CYGSSsS8NTOG8ka50bv68kzhwjcUxXUteLWh66q+nO9j1RVeaiaujbejJcW1HZ+ecD0U1sh4Z2s6w8PdmN7zql0vDEaXECjQTZvvHRjIqiP5HMisMrQ5V6S+RTfDc7Lu2GrUJjqe832oIr1a17Tteghx082408oaO/xcJjoeD3tLKhovX7zWGNBqBZ5dfwozsYg3pvcw2nSYLiNQAM+MiyDEzZbHfjphtDf/fKFVO0vjmy7rS6NcxZmSek4U1pFX1Yz2JlsfKaxpoVam6pRoTF8nK1xtpRw3wmadHU2jXEVKUT1J+bUU1cpuiHU4a6mElg5OTbgePt+TxaHsal6cFHnVsmaGpku9Ra2kZnx2Zy+mfHqAx9aeYNX8fh3aw6gtyJQ6gbK2MI5MbH1RqDWsSyxiXVLRJVFI9pYSxkV7cv/QYMJa2Qq6K3MkV1cNoKdfxzSh+ycikYi+Qc4cyKxCqxXatcWJMaJUa1mfXMSPRwtIKb44hcTeUsKYKE8WDAki0qtrVmKxkoppURmnQB3KruKDHRlMjfPm9j5+197BgHQpgQJdB8tXp3TnmfWneG97Os+OjzC0SRdxfjFdpel6o8AzJfU89ONxcquaifa25/HRYYR52GJpbkZFo5xjebX8mVLKhuPFPDoqlIdGhhita6A92JlajpeDZae4+EDX3mNzShnHC2vpHaB/q+2uQmGNjPtXJpJW1kiEpx1PjAkjzMMOC4mYsgY5Sfm1bEkp5dfjRdw/JJinx4V3uZQNrYDRDZ4BSupaeHTtCQJdbYzatXeeLidQALfF+3K8sI4v9mQT5GLDLCMaBZzvVSM30tHTlUjMq+Gub4/iYGXO9/f1YXiY2yUP7+19/Hl+YiSv/HGG93dk0KzU8NwE4xogtBe1zUr2pFdyRz//TvsRj4xwR2omZktK2Q0rUIU1MmZ+cQiFWsvXc+MZHel+yfc7p68//zcpire3pfHVvhzyq5v59I5eXUqklGqt0SVeN8pVzFt+jBalhh/m9+sSXRaM38LLIBKJeHVqNEW1Mp7fkIKPkxWDjKSs0PlSNc169EwyNJWNChasTMTLwYqfFw24amt6ZxspH90eh62FhGV7s+kf7MzwcPdOtLZz+O1EMUqNltGRHuRUNv0jiVaEg5U5jtbmbX5harQCTQo1TQo1zQo1YpEIC4kYC3MxPf0d+fV4MU+PD8dC0jXdxFdCEAQe++kELSoN6x8YeFU3sYO1OW9M70GImy2vbkrlwx0ZPGNk3pKrUdusxNGIAqXUGi0P/XiczIomvr+3z1XbpRgTXVKgQOdK++zOXtz6xSEWr0rihwX9jKK0kM+5BcfCmhZifB0Na0wreXdbGs0KNb8sHnhVcTqPSCTipVuiOZBVxfvbM7qsQNXU1DDr9tvJq1HgEhLDLXfcT1GDmrSyBvKqdeHed3179Ir721lKcLezIMzDjlAPO8I97OgT6HShlplGK3C2tIHEvBrSyxvJr5aRXy2jpL6FaxWNCH9xK738HXW9lzzsCPO0I9LTHicb43np6cuejEqS8mt5a0aPVq9hzhscxNnSBpbtzWZOX/8L4fjGTmXT5bswGwKtVuA/v6awN6OSN2f0YGhY53Vsvl66rEAB2Fuas/y+vtz+1WHu+vYoP8w3vEgFuOh+QHnVXaMCe32Lit9OlDC7j79eycVSiZi7+wfwvz/PklfVTGAXyvvKqmjkQGYVX2/cS3X8Q6gFCeXAt4cKCXK3vSBOvfwdmdbTh/8+9zSvv/4/7O3s0AoCDS0qappV1MqUlNS1kFbWyLYzZfwz+Ky0uJ5uz2++8G9nGykBLtb0DXLG18kKBytz7Cwl2FhI0AqgUGlQqLXIVRr+9+dZQDcQ2HK6jDUJhReOE+Fpx5BQVwaHutE30PmS9ufGzJaUUuwtJczsrV+PtCfGhvHr8WJ+OJLPfyZGdpB17YcgCORVNdMj1vC9vQRB4KWNZ1iXVMQjo0KZ09ff0CbpRZcWKABvRyvW3N+fOV8fMQqRsrGQ4GZncSFh19g5nF2FUq1lapy33vv2D3YB4Gxpg9ELVEG1jD9OlbDxRAnp5edyjWRmTIp3Z0R3P7wslNx362T+PJXCsHd3E+Bizc+LBiASifhv/jHGRbjg6np5N7IgCOzNqOSFDacprrs0OfP2eD+eHBvW6irRQa42zF+RyLSePtzVz5/KRgVpZY2kFNdzILOKFYfy+Xp/LlKJmNGR7szs5cvQMDejX6M5WVhPn0Bnve30crBiYDcX9mZUdgmBKm9Q0CBXG9yNptUKvLoplVVH8lk0NJjHR4ca1J620OUFCsDXydqoRCrC0+6S0FljJauiCYAob/3Ded3PuTCqmpXtalN7oVRr2XK6lFWH80nM1+UXxQc48cqUaEZGuNMj2JvPPqm7sH1leSlf7MmiolHBJ3N6Xli8F4lEjB07FpFIxKJFi1i4cOGFfXanVfD21jTSyhqxFGuxyjuERekJtFIVH90ex7qkQn5KLOS3E8Xc3T+ARcO6XdP1MzLCnX5Bzry3LZ0J3T1xt7fE3d6SoWFuLBkRgkypJiG3ht1pFWw8WcLmlDJcbaVMjfPhrv4BRlvFpFamJK6Nv8tobwe+3p+DIAhGH3l2vvNCuAFTMTRagefWn2JdUhHzBwfx3IQIo//eLscNIVBwsUjN+foIn8zpyahID4PY0j/YhXe3pVPTrMTZyNcM5CotYhFt6kPUfC4R0cpIum+ep0WpYU1CAV/ty6GsQY6ouQppQQKSkpOktdSRBji+/vol+4ldA/lsTzYzevnQ79zsEODgwYN4e3tTUVHBmDFjiIiIwCeyF69tSmVPeiVBrja8MzOGW2K9sZLeAkB8fDzTevowracPeVXNfLIri+8O5vJjQgHPjAtn7oDAK+Y6iUQiXp/enQkf7+fljWcuEkvQ3avh4e4MD3fnhUlR7EmvYH1yESsP5/HdwVzGRnnw0IhQevga3sX0T+ytzKmVtW0wY2ku7jIJvAm5NUjNxAYbJLcoNTz+0wm2ninjsdGhPDoqtEuKE9xAAgU6kVq/eCDzVyRy/8pEXrolmnsGBna6Hf2DdSHCCbnVjO/u1enn1wdrCzO0gi4E1c7SXK9908saAIymMK5ao2XtsUI+2plJVZOCfkHOvDmjB8PC3BCL77lkew8PD0pLS/Hy8iKnoAj7MUtwtZXy0uToi7bz9ta5P93d3Zk+fTor9qVzcEcz5mIxL06KZO6AQKSSK7utAl1teH9WLEtGdOOVP1J5+Y9U/kwpZemcnldsbxDibsejo0J5b3sGI8Ldr7huI5WIGRvtydhoTyoa5aw6nM+qI/lsO3OAcdEePDU2nFAjSar2d7Zu89qsTKkxurDtK3Ewu4o4P0eDtE2vaJRz/4pEThXX89/JUcwbbDzdcdtC17jjeuBub8lPi/ozKtKDlzae4eWNZ1BrtJ1qQw8fR+wsJOxIrejU87aF85n6bXFJ7jxbga2FhAgjCFk9lFXFhI/38+Jvpwl2teHnRQP4adEARkS4X3GmMmXKFFasWIFWKzD/630Idp68c2ssDtZ/C3VzczONjbo1q4bGJn7OMeOvJm/i/Bz568lhLBgSfFVx+ifBbrYsv68P790WS2pJA7d8cvCqpY0eGB5CvyBnXvztdKsadrrbWfLk2HD2PzOCx0eHcSirmgkf7+d/m1KNogtA7wAnMsqbKGxDQdyzpQ10c7c1+plAYY2M08UNjIzs/MjWMyX1TPv0IBnlTXx1d3yXFye4AQUKdC6QZXf1Zv7gIJYfymPO10core+8ysJSiZiJPbzYerr0QukjY6WnnyNmYhH7MvQrwFsvU7ElpZRJPbwMMlI8T51MyVPrTnLHN0dRarR8eXdvflrUn75B1050fe6559ixYwchMx4nV+XAEyMDGRbmRklJCRMnTgSgvLycwYMHExMbR69F7yHz7sWiocH8ML9fm1pji0Qibu3ty4Ylg7CWmnHXN0dJzLt8e3AzsYhP7uiJg5U5C1cmUd7QuvqTdpbmPDo6lL3PjOC2eF++PZjLqPf3sivNsP3UpvX0wUwsYtWRfL32q5epOJJTzaBuLtfe2MBsTikFYFKPzvWc/JxYyIzPD6EVYN3iAYyJMszyRntzQwoU6H7c/zc5io9nx5Fa0sCkpQfYk955M5oZvXxoVmrYfsa4myw6WksZEe7Gz4mFNOmRXPzZnixkKo1BXKjnOZytmyH8dryYB4d3Y9tjQxkX7dnqUbaLiwsL3vwebcQY5vT15+GxOteet7c3mzfrQsSDg4M5efIkM15bjdq/D4+NDuU/EyORXKe7KczDjnWLB+Bhb8m85cfIvULUp7udJd/cE0+dTMncbxOo02MNx9lGypszYvjtwUE420iZtzyR59afMlgSuY+jFeO7e7LmaAEVrRRb0L18VRqBqXHG2RLiPIIgsD65iFhfh07L12pWqHl63Ume+eUU8YFObHpkMN19jGvt8Xq4YQXqPFPjfNj48GDc7Sy49/tjvPpHaqfMavoE6vJd1iQUdPi5rpeHR4ZS06zkm/05rdr+TEk9yw/mMaOnb5ui/64XQRD4fE8Wd3xzBCtzMzY8OIhnxkfoPZP76VgBz29IYWiYG69Ojb6isG0/U8byQ3ncNyiQR0e1X6iuh70lK+b1xUws4oEfklCqL++K7u7jwNdz48mtauaOr49So2fUZKyfI78/NIjFw7rxc2Ih0z8/SE5lU3tcgt48NTYchUbLy3+cadX2jXIVn+/JYkioq9EFffybQ9nVZJQ3cfeAwE45X1J+LROX7ueX5CIeHhnCynn9cLU1juTg9uKGFyiAbm62/LZkEHf3D+C7g7mM/2g/h7I6tqeUWCzi3oGBHM2tISn/8i4cYyHWz5GJPTz5cm8O2dd4cTUp1Dz843Ecrc15fmLnl55RqrU8/csp3tmazi0x3mx6ZLDeLy5BEFj6VybPrk9hSKgbX93d+4q5OQ1yFc/9mkK0tz3/mRDZ7msgfs7WvHtrLGlljXx9lQHCwBBXvr4nnuzKJmZ9eVjvdRwLiRnPTYhg1fx+VDUpmfLpwU71KJwnyNWGR0eFsjmljJ8TC6+5/csbU6lvUfH0uPBOsO76+O5ALi42UibHdKx7T67S8M7WNG5bdgi1RuCnhQN4cmy4URanvV5uCoECsDQ347Vp3flpYX/EIrjjm6P859dTNHTg4vEd/fxxtpHy6a6sDjtHe/HfydFYmotZsjr5QtPFf9Oi1LBwZSJ51c0sndMTl04erdU2K7nr26P8klTE46PD+Hh2nN7h8XKVhkfXnuCDHRnM6OnD13N7X3Xm9f2BPGqalbw5o0ergyH0ZXSUB2OiPFi2N/uqbtZhYW6smNeXigY50z8/SHIbekcNCnHlj4cH4+9szYIVifySVHQ9preJRUODGRziygsbUtiXUXnF7dYnFbE+uYiHRoYafdmwpPxa/kqr4J6BgR26Jnsoq4rxH+3j8z3ZzOzly9bHhrRqvbWrctMI1Hn6Bbuw9bGhLBoazE/HChn53l7WJBR0SI6FtVTC/MFB7E6v5HB2dbsfvz3xdLBk6ZyeZFc2sWDFsUuarclVGu5fmcjhnGrenxV7oYpEZ1HZqOC2Lw9zoqCOj2fH8eho/XM7implzP7qCBtPlvD0uHDenxV71YKsWq3A2mMFDAtz6/AX5JIRITTK1fx2vPiq2/UPduHXBwdiJTXj9i8P8/3BXIRrFfb7Fz6OVvy0qD/9gp15at1Jvj2Qez2m643kXB3NEHc7Fq1KuuxMbmdqOc+uP0X/YGceGRnSqfbpiyAIvLH5LG52FszvoMi5whoZD65O4o5vjiIAqxf0493bYvVODelq3HQCBbrZ1H8mRvLbkkEEuljzn19TmLR0/1VHc21l/uAgfJ2seHnjGVSdHO6uL0NC3fjo9p4k5teyYOUx6mW6mVRVk4J7vkvgYHYV790ay/Se+tVSu16qmhTM+foIxbUtrJzfV+/FckEQ+P1EMRM+3k9meSPL7urFkhHX7mV1pqSB0no503rqXwZKX2J9HfB3tmZ32rXdbiHudvzx0GCGhbnxyh+p3L8yUa+gA9BF+n1/b18m9vDktU2prDyc10bL24aDlTkr5/UlyNWGecuPXXT+rafLePDHZKK97fl6bvx1B6R0NFtPl5GUX8uTY8LavYVFg1zFe9vSGfXBXnalVfD46DC2PTbUaLo3dDQifUdfV6FrpHn/C0EQ2HK6jLe2pFFQI2NIqCsPjwxt12nztjNlLFqVxIuTIlkwJLjdjttR/JpcxLPrT+HjaMWSESF8sCODmmYl79wa0+mRVHKVhjlfH+FsaQPL7+ur98wtv7qZlzeeYXd6Jb0DnPhwVhz+Lq2LsPrxqC6IYv8zI/SOyoqPjycxMVGvfZ5ed5I9GZUce2F0q7YXBIHvDubxztY0LM3NeH5iBLf19tOrG69Ko+XB1cnsSC3n49lxnX5/mxVqHl17nJ1nK5g7IAA7Swmf7c4m1s+RFff1MaqWFZejXqZi3Ef7cLAyZ/OjQ9ptHUimVLP8UB5f7s2hvkXF1Dhvnh0fYdTt2VuB3l/OTS9Q51GoNaw8lM+yvdlUNyuJD3DiwRHdGBF+aUM1fREEgQUrEtmfVcUfDw02eBHJ1nAoq4o7vvm71cQfD+kfjHC9aLUCD689zuaUUr64szfju3u2et8mhZqv9uWwbG82UjMxj40O5d6BgXqNxj/emcmHOzPIfmOi3i+etgjUB9vT+XR3Fhn/m6CXnTmVTTy7/hTH8mqJ8XXgpVui9Gp4qFBruPvbBE4U1PHj/f2ID+zcNQ2NVmDRqiR2ntWlZIS62/LHw4MNml/XGgRB4KE1x9l2uowNDw5ql99HnUzJysP5LD+kW/scEe7Gk2PDb5TQcb1fpMY9d+5ELCRm3D80mAPPjuSVKdGU1suZtzyRiUsP8PuJYhTqtnfIFYlEvDUzBntLCY+sOW703XYPZlXx4m+nL/q/lzae5mxpQ6fasXRXJn+eKuW58RGtFqcGuYpP/spk8Nu7WPpXJhO6e16o+KCvq0jbfoO3ViOA3gOiYDdbfl40gI9uj6O8Qc7MLw5z3/cJnCysa9X+FhIzvryrNz5OViz+IUlvd+H1oFRr+XJfNvsz/3avZ1c28c7WdGqNtAjxeX47Ucyfp0p5fEzYdYtTblUzr/6RysC3dvHBjgxifR1Y/8AAvr+v740iTm3CNIO6AiqNlt9PlPDFniyyK5txsjZnRi9fbu/j1+pma/9md3oF931/jJm9fHnvthijK9tyLK+GD3dkcCi7Gn9na16f3p3BIa5sOF7M//48S61MycTuXiwZEdLh+U+JeTXM+vIw03r68P5tsdf8rgqqZfyUWMDKw/k0ytWMjnTn4ZGh11Ww8+fEQp755RS7nhxGsJt+9QbbMoN68ueT7M2oIPHFMXrt909kSjUrDuXz5b5s6mQqegc4cXf/ACb08Lxmh97M8kamfHqQWD8HVi/o36Fhywq1hp8Ti1i2J5viuhYmdPfk5SnRWJqb8daWNH46VoCNVMLi4d2YNyjI6PpeZZQ3MuPzQ0R42vHTogFt+q5UGi1/na1g9dF89mdWIRGLmBzjxaJh3S6UILvBMLn42hutVmBfZiU/JxayI7UclUagp78jt8f7Mb67p94+8o92ZvDRzkyeHR/BA8O7dZDVrUdz7vq+O5DL/swqXG0teGB4N+7s53+Ri6W2Wck3B3JYcSifJoWakRHu3N7HjxHh7u0eft0oVzFx6X5EiNj86BBsr7DwLFdp2HamjJ+OFXIouxqRCMZGefDwyNB2GXWmljQwcel+3prRg9l6NnrTV6AEQWDIO7uJ8rLnq7nx+pp6CY1yFT8dK2T10QJyq5pxtpEyK96P6T19CPO4ck27dYmFPP3LqQ5bLy2skbEuqYifjhVQ3qCgl78jj44OY9i/urxmlDfyztZ0dp4tx9HanDl9/bmrf8CFjtWGpKZZydTPDtCi1LLxoUF6rQsJgsCpono2HC9m48kSapqVeDlYckdff27v49em8lldCJNAdSTVTQo2HC/mp2OFZFY0YSYW0T/YmXHRnoyN8sTT4doPlyAIPLL2BJtOlfDhrDim9TRM+ZbiuhZ+O17MmoQCimpbcLW1YNHQYO7qH3DV0Wq9TMWKw3msPJxPVZMCZxspt8R4MTzCnf5BLu0y0n1+QwprEwpYt3jAJWspRbUydqdVsDu9kkPZVchVWvycrZjV24+ZvX3bdRFZEARGfbAXBytzfn1goF4zXn0Fal9GJXO/S+CDWbHM6NV+UZJarcCh7GpWHcljR2o5WkHX9XlMpAdjoz3p6e94UZKyIAjcvzKJ/ZmVbHtsaLs0oiyolrE7vYKtp8s4nKMbSAwOcWXxsG4M7OZy1e81Kb+Gr/flsj21DIBx0Z7M6uPH4BBXgzRorJMpuePro2RVNvHTwv709He65j4arUBSfi1bT5ex7UwZxXUtSCVixkR6ML2nD8PD3Yw+UrGdMAlUZyAIAinF9Ww7U8bW02VkV+rqqEV72zMg2IUB3VzoE+SM/RVyFOQqDfOWH+NITjWfzOnFpA7OPD9vc3ZlM3+dLWfz6bIL6xMDgl24s78/Y6M89ZoJqTVa9mVWsj6pmJ1ny1GotUglYvoFOdPTz5FoHwe6+zjg7WCp14s9taSBSZ/s576BQTw6KpSsykZOFtZzqqiOk0X1F2rW+TtbMzLCnbHRHvQPctErck0fVh3J5/9+O83nd/Zioh4FQPURKJVGy9RPD1LdrGDfMyOu6YprKxWNcnamVrA9tYxDWdUoNVqszM3oFeBIL38norzsifK2x9xMzNgP99E3yJnv7u2j1znkKg2ppQ2cLq7nVFE9yfm15Jy7Z8FuNkyP82FGb1+9Z0JFtTJ+OFLA2mMF1MlUuNhIGRPlwehIDwaFuHaKC7BBruKub46SVtrIV3N7Mzz88hXLBUEgt6qZg1lVHMiq4nB2NQ1yNVKJmKGhroyN9mRctCcOVjd2DtNlMAmUIciqaGTbmXL2Z1aSXFCHUq1rAtjDx4FeAU5EezsQ5WVPqIfthVGfTKlm7rcJnCis451bY9p11Aw6AcmtauZYXi1Hcqo5klNNRaMC0Nk1oYcnE7t7tcsIWa7SkJBbw96MSg5mVZFR3sj5vGdbCwk+jlZ4O1ri6WCFrYUZ1lIJ1lIzpBIxWkG3f6NcTaNcxeqjl69d6GFvQQ8fR/oHOzMiwp1gV5tOWcNTa7RM+fQgRbUyfn9ocKu71eojUP/blMo3B3JZdlevTusf1ihXcSCziqO5NRzNrSG9rOHCPTMTiy4krrvZWXBLjDdWUjGWEjMszc0QiXRVRVpUGmRKDdXNSkrqWiipa6G8QX7hOC42UmJ8HRgW5sbwcPd2edYUag170yvZeLKEPemVNCnUSM3EdPexJz7Qmd4BTsQHOLV7lZP6FhX3fp/A6eJ6lt3V+6JmqDXNSlKK60kpquNUkU6Yy84Fmvg4WjE4xJUhYa4MD3e/orv6JsEkUIZGrtKQXFDLkexqDudUk1Jcj1ylS9CVmokJ9bClm5stvk5WOFqb88bmNAAeGRnC42PC9HrpqjVayhsVlNa1UFIvp7SuhayKJtLKGskob0Rxrviom50FA4Jd6B/swpBQ1w6vtNyi1JBW1sDpkgayyhspqZdfeHk1K3Qvtn9jbiZCpfn7EZo7IAA/J2sCXW2I8XXAw4C++YJqGVM/O4CtpYTl9/WlWysCJlojUIIg8PFfmXy0M5N7BgTwytTu7WWy3shVGtLLGkkra6CwpoXc6mb+PKVrHWEjNUOu1l5SbUUiFmElNcPJWnpuEGKFj5MVUV72xPg64KXn7FlflGotCbk17M+qJCmvllNF9SjPJcP7OVsR7mFHqIcd/s7W+DpZ4eNohaeDJVbmZnrZlVXRyK3LDlMnUzE5xotIL3sKa2QU1MjIr5ZRXPd3K59gVxu6+zjQN8iZwSGuBLhYG10wlAExCZSxodHqpvtnSupJLW0gtaSBvOpmSuvkqC9TXslGaoabnQX2VuaYm4kRASIRiBCh0mppVqhpVmhoUuhmHP8+hKutlEgveyI87YjwtCfWz5Fubp0z22gtWq1Ai0pzbqYpwsJcjKW52bkRagMHn+s4N1dbOVlYx7zlx1BrBd6Y3oOJPa7e1uNaAlXTrOTF31LYnFLGjJ4+vHtbrNEV+zzv3vxxQT8Ghrii0mhpUWkQtGB1bgZsTMhVGk4X15OYX0tKUT0Z5Y3kVjVf8juTSsQ4W0uxs5RgaW6GpbkYiViMVhAQBFBptTTK1TS0qC54Hf6Nq60F/s5W+DlbE+VlTw9fnUv7Sm59E4BJoLoO52c/RedGYs9vSLkwg4jzc8TJ2hyVRkBAQKsFAQFzMzE2Ugk2FhJsLcxwsDLHy9EKLwdLvM/93VVrc2VVNDL6g308MSaMR9qxpUV7UlAt48Efkzhd3MDQMDceHRVyxYTYKwlUs0LNisN5fL0vhyaFmifGhLN4WLBRDSDOo1BrGPjmLnoFOPF1O0QWGoJ//s6KaluoaFRQJ1NS06ykUa5GrtagUGlRa7WIRCLEIpCIxdhZSthyuuzCceYPDqJ/sAv+ztb4OVvpXaTYBGASqK7NrrRyHv/pJFqtwP9NjuK2eF+jfHF1BC/+lsLPiUUcfm5kp1dJ1we1RsvyQ3l8ujuLOpmKCE87JnT3on+wM9E+DhfWGM4LlEYrUFLXQnJBLXvTK9l2poxmpYbh4W48Oz7C6PNd3t6axpd7szn43Ei8HAwf4t0ZVDTKeXrdKfZmVDIqwp0PZ8eZZkbtg0mgujqFNTKeXHeShNwaBoe48uaMHp3WnfOf1MmU/JlSyoHMKs6WNlDXosLBypyB3Vx4ZFRou76slGotfV7fyfBwNz6e3bPdjtuRyJRqfkkqYuOJEhLzdW0vRCJdEVQnaynJHy8m9uEvKK1vuTAzdrAyZ0J3T2b39SfuOhKIO5O8qmaGv7enQ/Kifj9RzOqjBeRUNmMmBk8HK/oF6dI2evk7dvrgTKsV+DmxkDe3pKFQa3hhUhR39fO/aQaJnYBJoG4EtFqB1QkFvLX5LBpBYP7gIBYP69Yp7rvqJgWf7c5m9dF8FGotPo5WxPk74mwtpbJRwZ6MClxsLNjxxNB2c3PsSa/g3u+P8c3ceEZHeVx7ByOjqklBSlE9p4vrqWxSUCtTsfb5O5nzxmq8Ha0IcLEm2tueaG8Ho1tnag2Tlu5HKhGz4cFB7XbM8+tboe629PJ3QkAgr1rGiYI6lBot3X3seWps+BVDudubw9nVvLMtjeMFdfQLcuaNGT1aFQzz/+3deXjU5bn/8fcsmUlmsu/LhCQkZCERAgmbQIQqIovGVLFo9ViUqpWj1nNKT9XaxaU/7aH+WlGr2FY8akFRLKBsisguIUAC2QPZ18meSTKZ/fwRQDwJsiWZL5nndV1eEBySWzOZz3yf7/Pct3BZRECNJnUdRl7eVszmvHoCtCoev3EcP5oSOWxNNLfk1fObTfl09VnJmhTBT66PHtCRYXt+A4+8f4wPlk8bspb/v9tcwLrsavJ+e7PkG4ReqitpdSRVq3eV8acvSjn27Dz8tUPTXfyuNw/RabQM6ADebeqfifW3feVUtvZyS3IoL2SlDNso8/y6Tv64o4S9pc2EervznzfHc2ea6yytjzDRLHY0ifD14NW7J7FpxUzigj357eYCZr28m9d3n6Kjd+gaaVptdn6/pYDH1h1nTICWbU/MZtWSiYO2Czpc0YZMBpF+Q7fsePB0C9PGBoyacBptZsT2jzjJrmgbss85JkBDTXsvDZ3G7/y5p1rJvdOj2PFkBivnJ7C7RE/mawcorB+6RsV2u4PdJXoeXHuExav3c6K2g6cXJvL1yjksSY8U4SQhIqCuARMjfVn/0HT++dNpjA/35r93lDD1D7t4Yv1xDp5uwX4V04BtdgdPfJjLOwcqeWBmDJ88MmPQZrhWm53/3lHMOwcq+fG0MZc8U+li+iw2Tum7SR3hUR7CpZug80WtlHO4YuimQj/2gzgUMhn3vH140C75aqWCFXPj+PiR67HZHdz55kFyKq8uIFu7Tby15zRzVn3NsneOkFfbyRM3jmPvL+fyUEaseIMkQWKJ7xpU1NDFuuxqPj1eh6HPSqi3O7ekhHLz+BDSov0u+QyRw+Hg6U9Psi67hqcWJPLwDQOb15qsNnYWNPHqrjLK9N38KD2SF7NShqx3WF5NB5mvHxjRLgojYTQt8QHc8deDKOQyPnp4xpB9ztyaDpa/m0NHr5m7pkTySEbsoG989F19LF3zDc0GEx8+POOyOulXtvTwZVETOwubyKlsw+6AaTH+3Dcj6rLbewlXTdyDciVnu3l/fqKBPaXNmKx23N3kTIn2Z4LOh5Tw/sODOj+PQZctzt6oXjE3lpXzE4H+0GruNnGsqoN9Zc1sPdlAe6+FmEAtv1qQyPzkSx8aeCnWZVfz1MaT7Fk5h6iAq2+FIxWjLaCe2niCHQVNHHv2ykeBDKa128RfdpWxLrsai83B1Gh/fpAUzPSxAaSEe597I1TXYeSONw7i7ibns8cH73DfZ7FR1tRNbk07x2s6yK3uONcHMDHUi3njQ7h1YvgVj8sRrpoIKFfVY7Jy6HQr+0+18E15K2X67nOtabzUSsYEaAjzccdPo8JPq6KqtYcdBf0TTO9K19FjsqE39FGm76aj1wKARqVgTkIQS6eMYWZc4LDsQPt/W4t450Alxc/fMmwNX51htAXUm3tO89K2YvJ/P39Y+sk1dBrZeKyOTbl1lDZ1A/2tlHR+HowJ0BLh686J2k4KztyLejhjLL1mGx1GC7XtvdS0GWnp/rbrQ6CnitRIX66PDWTe+BCnHNUQBrjsH3BxHHqU0KqV3DQ+5Nw27bO91fLrOyluMFDT3kt9Rx/5dV2095rP9ekD+LqkGS93Jf5aFQtSwogP8SQ53IfUSN9hXwLpNFrw0biNqnAajc7uomvrNg9LQIX5eLBibhwr5sahN/SRXdFGQX0X1a39nVYK67swndfD8a295fhp3PD2cEPn58GNicHo/DyICdIyUed7wVUD4doiAmqUcndTMDHSd9CJsruL9Sxbe4TfLB7PA7NiRr6483SeOQAsSFuAZ//28uZu05BtkLmQYC93Fk8IZ/GE8AH/zmi2MWfVbsJ8PPj00cub0SVce8QdQhf02u5TRPp7cO/0KGeXQlefBW9357xP2rBhA8nJycjl8u9djtu+fTsJCQnExcXx0ksvjWCF0qE5s8PNNEgn+pHkoVLwH/Piya3p4ODpodtVKEiTCCgXU9pk4GhVO/fPiJbEDibzmUGHzpCSksLGjRvJyMi44GNsNhsrVqxg27ZtFBYWsm7dOgoLC0ewSmk4uwR7FScahkxmagQ+Hm6sP1Lj7FKEYeb8VyhhRG3OrUcu6/8hlwKNSonR7Jx35UlJSSQkJHzvY7Kzs4mLi2Ps2LGoVCqWLl3Kpk2bRqhC6Ti74UYKtwrd3RRkTYpgR34j3Sars8sRhpEIKBezu0TPlGh/gryk0THcU62U9ItMXV0dkZGR5z7W6XTU1dUN+tg1a9aQnp5Oeno6zc3NI1XiiDD09X+PpDLO5cakYMw2O0fPNOoVRicRUC6k02ihsKHrXOsaKdCqFcMaUDfddBMpKSkD/rnUq6DBjmFc6Mb8Qw89RE5ODjk5OQQFBV1V3VLT3tPfWstXI42ASovyQymXcbhc3IcazcQuPhdS1mTA4YAJEmorFOLtTrPBhMVmx22IulOc78svv7yqv6/T6aip+fZeR21tLeHhA3eXjXa1HUZksv7vlxRoVEqSI3w4Vi2uoEYzcQXlQs6eqh8bKJ0xApH+GuyO/jlYUjRlyhTKysqoqKjAbDazfv16brvtNmeXNeKqW3sI83aXxMaas2IDtVS3SvN5IwwN6TzbhGHXbOg/aR/qI413wQBJof191YoaDCP+tT/99FN0Oh2HDh1i0aJFzJ8/H4D6+noWLlwIgFKp5LXXXmP+/PkkJSVx1113kZycPOK1OltRg4FEiU3/DfVxp8lguvgDhWuWWOJzIT0mK24KGWoJvQuOD/VEKZeRX9/Jogkj2yw2KyuLrKysAX8eHh7O1q1bz328cOHCc4HlioxmG6eau5knsWGS7m4KbHYHNrvjmhwEKVycdF6phGFnd4AMmaRO36uVCpIjfIZ01pAwtHKq2rDZHaRF+zm7lO84e8/SfF7bLmF0EQHlQrQqBWabHYtNWj/QM2MDyK3pkPR2c1d28HQrSrmMqdH+zi7lO4wWGzIZuCmk84ZLGFoioFyI9kyTz7NnWqQiIz4Im93BnpLRdXZotPiysIm0KL9zzx+paOk24a9RDdlsMkF6xHfWhYw5M3KgsrXHyZV815RofwI91Ww92eDsUoT/o6TRQJm+e8TvD16KZoPpXJd1YXQSAeVCzg5qK20c+R1z30chl7EgJZRdxU109VmcXY5wni15/a2xFkhw2nFxYxexwaNnyKUwkAgoF6Lz88DDTUGxxAIKYEm6jj6LnU3HB28jJIw8k9XG+iM1ZMQHSaY11lltPWZq2oxM0Pk6uxRhGImAciFyuYwJOh+OVEpvx9wEnS8pEd78z6Eq7FJomS3wWV4DLd0mHpjp3Jlhg8mt6e8gIaWuKMLQEwHlYmaPC6SgvuvcoV0pWT5rLGX6bnYV651distzOBz8fX8F44I9mT0u0NnlDLC7uBkPNwWTx0hr67swtERAuZizI+G35UtvQ8LiCWFE+nvw2u5TgzZpFUbO16XNFDZ08cCsGEmdmwOw2OzsKGhk9rhA3M8MUhRGJxFQLiYx1JuEEC82HpPevR6lQs6jc+LIq+lgR0Gjs8txWTa7g5e2FhMVoOGOyTpnlzPAriI9eoOJJemRF3+wcE0TAeWC7p4aSW5NhyRn6SxJ0zEu2JOXthWLDgFO8vHRGkqaDPzXLYmSag571geHqwjzcWduwugaaSIMJL1nnzDslqRH4u2u5G/7yp1dygBKhZxnFiVR2drL2xKsb7Tr7LWwamcpk8f4siAl1NnlDFDR0sO+shaWThkjDui6APEddkFatZJ7p0exvaCR083dzi5ngDkJwSy8LpS/7CqjXIL1jWa/31JAe4+Z5zJTJHfvCWD1rjLUSjl3TxXLe65ABJSLWjYzBq1KyYufFzm7lEH97tZk1Eo5//XJCawS6x04Wu0saGTj8TpWzI0jJUJ627eLG7v4V24d918fTbBEBicKw0sElIsK8lLz+I1xfFWsZ3eJ9LZ1B3u781xmMkcq23n1q1POLmfUa+sx8/Sn+YwP82bF3DhnlzOA3e7gqY0n8dWo+NkNsc4uRxghIqBc2E+uj2FsoJbntxTSZ7E5u5wBsibpuGOyjtVflXHwdIuzyxm1rDY7j607RpfRwqolEyW7MeJ4dQfPLk7CT6tydjnCCJHeM1EYMSqlnN/dlkx5Sw8vbSt2djmDei4zmZhALY+vO05dh9HZ5YxKL3xexIFTrfzhh9cxPlxaU3MBGjv7eHl7CbPHBXJ7aoSzyxFGkAgoF5cRH8SymdGsPVjJl4VNzi5nAK1ayZr70jBZ7Ty49oiYGTXE1mdXs/ZgJctnxXBnmvTOPFlsdh5ffxyr3c4Lt0tz44YwfERACfxqQSLJ4d6s/DiPhk7pXaXEBXvx+j2TKdN38/i645IbuHitOlzeyrOb8smID+JXCxKdXc6gXt5WTHZFGy/9cAJRAaJzuasRASWgVipYffckTFY7D793FKNZevejMuKDeC4zma+K9fxiQ55oKHuVTtZ2svzdHCL9NaxeOkmSZ4q25NXzt/0V/OT6aG6fJJb2XJH0npWCU4wN8uTVpZM4WdfJkx/mYpNgAPx4WhQr5yewKbeeZ/51UoTUFSpq6OLf/nEYbw833n9wGj4aN2eXNMDh8lZWfpxHepQfTy9McnY5gpOIgBLOuWl8CL9eNJ7tBY08vVGaAbBibhwr5sayLruGX2zIE2ekLlNeTQdL13yDWqngg+XTCPf1cHZJA+TVdPDguzlE+Hrw1n1pktxVKIwMpbMLEKTlwVkxdPSaWf3VKTxUCn5763jJ3Zj+xc0JuCsV/OmLUowWG39emopaKbpaX8w35a0sfzcHP60b/1w+nUh/jbNLGqCk0cD972Tjp3Xjg+XTCRAj3V2aCChhgP+YF0+v2cbf91dgsvbvnlLIpRNSMpmMx24ch0at5PnPCmn9ezZv3Zsmzsd8j49yanjm05OM8dfw/vJphPlI78rpZG0ny9Zmo1LI+eDB6YT6iG4Rrk5cOwsDyGQyfr0oiUfnxLIuu5rH1x+X5EHeB2fF8JelqeTWdJD1xgHRt28QNruDFz4r5Jcfn2BaTAAbfzZTkuG0p7SZH605hFqpYN1D0xkTIL2rO2HkiYASBiWTyfjlLYk8vTCRz080cM/b39DaLb0pvJmpEaz76TS6+qxkvnZAzJE6j6HPwvJ3j/C3/RXcPyOKtcumSHJDxMdHa3lw7RGiArRsfPR6YoM8nV2SIBEioITv9VBGLG/8eDIF9V3c9toBTtZ2OrukAdKi/Nn87zMZG6Tl4feO8oetRZd0VmrDhg0kJycjl8vJycm54OOio6O57rrrSE1NJT09fShLHzZHq9pZvHo/+8paeOH2FH6fmSK5reRmq53fbS7gFxvymDbWn48enk6IaAIrnEdaz1hBkhZeF8ZHD8/A4XBwx5sHWZddLbmR7Do/DR89MoN7p49hzd5yfvjGQU7pDd/7d1JSUti4cSMZGRkX/fy7d+8mNzf3e4NMCiw2O698UcqSNw9itTn450+nc+/0KGeXNUB9h5EfrTnE2oOVPDgrhrXLpuLlLr2rO8G5REAJl2RipC+fPT6baTH+PLXxJI9+cIz2HrOzy/oOtVLBC7dfx19/PJna9l4Wvbqff+yvuOB2+aSkJBISEka4yuFT3tzNnX89yKu7yrh9UgTbfj6bqTH+zi5rgK0nG1i8ej+ljQZev2cyzy4ej5vEru4EaRDPCuGS+WtVvLtsKk8tSOTLoibm/3kv2/MbJHc1teC6MHY8mcGsuECe+6yQu946RHFj1xV/PplMxs0330xaWhpr1qy54OPWrFlDeno66enpNDc3X/HXu1wmq42/fn2aRa/up7K1l9fvmcwrd6XiLbErkpZuE49+cJRHPzhGhK8Hmx+bxaIJYc4uS5Aw2RC+uEjrVUoYVvl1naz8+ARFDV3clBTCc5nJkjv06XA4mLb0CfQRs0DpjlvFAVSlXyCzmXnxxRfJzMwEYM6cOaxateqC95fq6+sJDw9Hr9czb948Vq9efdFlwfT09BFZDtxdoue5LYVUtPRwU1IIL9yeIrnt2Q6Hgy0nGvjtpnx6TDaeuGkcD2eMldw9MWHYXfZZFXEOSrgiKRE+bPn3mfzjQAX//4sy5r2yhyfnxXPfjCjJHJqVyWRkf/gq7T1mXt5ezHq5At/UeTxx4zgWTrn0keHh4eEABAcHk5WVRXZ29iXdtxpOVa09PP9ZIV8W6RkbqGXtsinMSQh2ak2Dya/r5IXPC/mmvI2Jkb6sunMC40K8nF2WcI0Qb2GEK6ZUyHkoI5adT2YwNcafFz4v4ger9vDJ0VpJ9fLz06p46Y4JfPKz64ny1/Drf+Uz75U9bMmrv2g7p56eHgwGw7nf79y5k5SUlJEoe1ANnUZ+symfea/s5dDpVn61IJHtP8+QXDjpu/pYuSGPW1/bT2lTN89nJvPJIzNEOAmXRSzxCUNmX1kzL28vJr+ui4QQL1bOT+DGpGBJtUpyOBx8Vaznj9tLKGky4Girpn3/P/FoKyN14kR27NhBfX09y5cvZ+vWrZSXl5OVlQWA1Wrlnnvu4Zlnnrno1xnqJb76DiNvfH2Kj47UYnc4uDNNx5Pz4iW3LVvf1cfb+8p5/5tqrHY7y2bGsGJuHD4e0rofJjjFZb8QiIAShpTd7mBrfgN/2llKRUsPE3U+PHJDLDcnh0qqXZLN7mBzXh2vfFFKTZuRqAAND8yMYUm6Do3q6le+hyqgSpsMvHOgko+P1gBwZ1okj86JlVwfvboOI2/tOc36IzVYbXZumxjOk/PixQwn4XwioARpsNjsfHy0ljf3nKaqtZeYQC3/NiOKO9J0ktpdZrXZ2VHQxNv7ysmt6cDHw417po3h/hnRV7XZ4GoCymKzs6OgkfcOVXG4og2VQs6SdB2Pzo0jQkIbURwOB8eq23nvUBWfnWhAJoM703Q8ckOsCCZhMCKgBGmx2R3sKGhkzd7+ANCoFNw+KYIlaTpSI30ltfx3tKqdv+8vZ3t+IzKZjDnxQWRNjuCmpBDc3S5v48eVBFRdh5EPj9SwLruaZoMJnZ8H906PYkmaTlJdvbtNVjbl1vHeoSqKGw14qZXcma7jp7PHSm4npyApIqAE6TpZ28l731SyKbcek9XOGH8NmanhZKaGExcsnZvnNW29vH+4ik3H62ns6sPLXcmi68LImhTBlGh/5JewVHmpAdVsMLH1ZAOfnajnSGU7MhnMTQjmvulRZMQHSWZZ1GS18XVJM5tz6/myqAmT1c74MG/umxFFZmr4kCyLCqOeCChB+rr6LOzIb2RzXj0HTrVgd8D4MG9unRjO3MQgEkK8JHFlZbM7+Ka8lU+O1bI9v5Fes40QbzVzE4KZmxjMzLhAPNWDvzBfKKAcDgcVLT3sLW3mi6ImDp1uxe6AhBAvbp0YRmZqhGTuLxn6LBw41cKuIj3bCxox9FkJ0KpYNCGM2ydFMEliV8CC5ImAEq4tekMfn59oYFNuPbk1HQAEe6mZPS6IjPhAZsUFSmJ5q9dsZWdBEzsLG9lX2oLBZMVNIWNqjD9zE4KZkxBEbJDnuRfs8wPK0Gfh4OlW9pY2s6e0mdp2IwBjA7UsnhDG4onhxEtg+7Xd7qBUb2BPSTO7S/TkVLZjtTvwUiuZlxxCZmoEM2MDxAFb4UqJgBKuXfUdRvaXtbC3rJn9p1ro6LUAkBzuzZRofyaN8WVSpB+R/h5OfedusdnJqWzn6xI9XxXrKdP3z6EK0KqYNMaPIC8Va1fezd1/+IBSvYHiBgNWuwOtSsGM2EBuSAjihnFBTp95ZDTbOFHbQU5VO0er2jlW3X7u/3liqBdzEoKZmxDE5Cg/0StPGAoioITRwWZ3kF/Xyb4zYZVX04nxzNBEX40bCSFeJIZ6kRDqTXyIJ2MCNAR5qkcsuBwOB01dJk7pu9lTqufdg1WYzxvx0fDuzwm7/8/nPp4ZF0DWJB3jgj2JCtDgqxm56b99Fhu17UZO6Q0UNRgoaTRQ0mSgsrWHsz/+Y4O0pEf5kR7tz+xxgZIcaihc80RACaOT1WantKmb4zXt5Nd1UdLYRUmjgR7zt5N+PdwUjPHXEOHnQZCnmkAv1Zlf1Xi7u6FVK/FUK9GoFKiUchRyGcozmxD6LHZMVtt3fu2z2GjvNdPWY6a9x4zeYKK+s4+GDiP1HcbvfG0vdyVxwZ4khnqj8/Pgj49k8eTrn1DU0EV+XRd1Hcbv/Pf4eLgRHaBB598frIGeKgI81fhrVfh4uKFRKdCo+mtVKmTIZTJkgFwmw2p3YLbZMVn66+w0WujoNdPea6G999taa9p7qW030mz4dtCkTAbRAVoSQrxICPUiJcKHtCg//LUjF5iCyxIBJbgOu91BXYeRU/puqtt6qW7rpaq1l4ZOIy3dJlq6zUPWckkmgwCtmnBfd8J9PAjzdWdsoJbYYE/igj0HXL39300SfRYbNW29VLb2UtXaQ2VrD1WtvdS09dLabcZgsg5JndAf1EFeaiL9PdD5atD5eRDh50FskCfxIV54qKTRK1FwOaJZrOA65HIZkf6aC+56s9sdtPeaaek2Y+iz0G2y0m2y0muyYbU7sNntWO0OHA5wd1Pg7iZHrfzur74aN/y1anw83K5qy7e7m4JxIV4X7EVnstpo6zHTYuivtddso8dsxWi2YbE7wOHA7gC7w4FCLsNdqUDtJketlOPt4YafRoWfRoWvxu2yz2wJglSJgBJGLblcRoCnWhK7AC9GrVQQ5uMh7v0IwnnE1hxBEARBkkRACYIgCJIkAkoQBEGQJBFQgiAIgiSJgBIEQRAkSQSUIAiCIEkioARBEARJEgElCIIgSJIIKEEQBEGSREAJgiAIkjSUzWIFQThDJpNtdzgctzi7DkG4lomAEgRBECRJLPEJgiAIkiQCShAEQZAkEVCCIAiCJImAEgRBECRJBJQgCIIgSf8LTMiMk1/nh4QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x11b676f4a30>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = sy.symbols('u')\n",
    "xc=sy.cos(u)+sy.cos(7*u)/2+sy.cos(17*u)/3\n",
    "yc=sy.sin(u)+sy.sin(7*u)/2+sy.sin(17*u)/3\n",
    "syp.plot_parametric(xc,yc,(u,0,2*sy.pi))#使用 SymPy 的 plot_parametric 函数绘制参数化曲线。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x11b677c3c10>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy as sy\n",
    "import sympy.plotting as syp\n",
    "\n",
    "# 定义符号变量\n",
    "u = sy.symbols('u')\n",
    "\n",
    "# 定义参数化曲线的 x 和 y 组件\n",
    "xc = sy.cos(u) + sy.cos(7*u) / 2 + sy.cos(17*u) / 3\n",
    "yc = sy.sin(u) + sy.sin(7*u) / 2 + sy.sin(17*u) / 3\n",
    "\n",
    "# 绘制参数化曲线\n",
    "syp.plot_parametric(xc, yc, (u, 0, 2 * sy.pi))#该函数接受三个参数：x 组件的表达式,y 组件的表达式,指定参数 u 的范围，从 0 到 2π。这将绘制一整圈\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 二维画图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-I*sin(x**2 - y**2)*sinh(2*x*y) + cos(x**2 - y**2)*cosh(2*x*y)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x11b67867eb0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Exception in callback BaseSelectorEventLoop._read_from_self()\n",
      "handle: <Handle BaseSelectorEventLoop._read_from_self()>\n",
      "Traceback (most recent call last):\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\events.py\", line 80, in _run\n",
      "    self._context.run(self._callback, *self._args)\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\selector_events.py\", line 115, in _read_from_self\n",
      "    data = self._ssock.recv(4096)\n",
      "ConnectionResetError: [WinError 10054] 远程主机强迫关闭了一个现有的连接。\n",
      "Exception in callback BaseSelectorEventLoop._read_from_self()\n",
      "handle: <Handle BaseSelectorEventLoop._read_from_self()>\n",
      "Traceback (most recent call last):\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\events.py\", line 80, in _run\n",
      "    self._context.run(self._callback, *self._args)\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\selector_events.py\", line 115, in _read_from_self\n",
      "    data = self._ssock.recv(4096)\n",
      "ConnectionResetError: [WinError 10054] 远程主机强迫关闭了一个现有的连接。\n",
      "Exception in callback BaseSelectorEventLoop._read_from_self()\n",
      "handle: <Handle BaseSelectorEventLoop._read_from_self()>\n",
      "Traceback (most recent call last):\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\events.py\", line 80, in _run\n",
      "    self._context.run(self._callback, *self._args)\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\selector_events.py\", line 115, in _read_from_self\n",
      "    data = self._ssock.recv(4096)\n",
      "ConnectionResetError: [WinError 10054] 远程主机强迫关闭了一个现有的连接。\n",
      "Exception in callback BaseSelectorEventLoop._read_from_self()\n",
      "handle: <Handle BaseSelectorEventLoop._read_from_self()>\n",
      "Traceback (most recent call last):\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\events.py\", line 80, in _run\n",
      "    self._context.run(self._callback, *self._args)\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\selector_events.py\", line 115, in _read_from_self\n",
      "    data = self._ssock.recv(4096)\n",
      "ConnectionResetError: [WinError 10054] 远程主机强迫关闭了一个现有的连接。\n",
      "Exception in callback BaseSelectorEventLoop._read_from_self()\n",
      "handle: <Handle BaseSelectorEventLoop._read_from_self()>\n",
      "Traceback (most recent call last):\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\events.py\", line 80, in _run\n",
      "    self._context.run(self._callback, *self._args)\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\selector_events.py\", line 115, in _read_from_self\n",
      "    data = self._ssock.recv(4096)\n",
      "ConnectionResetError: [WinError 10054] 远程主机强迫关闭了一个现有的连接。\n",
      "Exception in callback BaseSelectorEventLoop._read_from_self()\n",
      "handle: <Handle BaseSelectorEventLoop._read_from_self()>\n",
      "Traceback (most recent call last):\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\events.py\", line 80, in _run\n",
      "    self._context.run(self._callback, *self._args)\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\selector_events.py\", line 115, in _read_from_self\n",
      "    data = self._ssock.recv(4096)\n",
      "ConnectionResetError: [WinError 10054] 远程主机强迫关闭了一个现有的连接。\n",
      "Exception in callback BaseSelectorEventLoop._read_from_self()\n",
      "handle: <Handle BaseSelectorEventLoop._read_from_self()>\n",
      "Traceback (most recent call last):\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\events.py\", line 80, in _run\n",
      "    self._context.run(self._callback, *self._args)\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\selector_events.py\", line 115, in _read_from_self\n",
      "    data = self._ssock.recv(4096)\n",
      "ConnectionResetError: [WinError 10054] 远程主机强迫关闭了一个现有的连接。\n",
      "Exception in callback BaseSelectorEventLoop._read_from_self()\n",
      "handle: <Handle BaseSelectorEventLoop._read_from_self()>\n",
      "Traceback (most recent call last):\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\events.py\", line 80, in _run\n",
      "    self._context.run(self._callback, *self._args)\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\selector_events.py\", line 115, in _read_from_self\n",
      "    data = self._ssock.recv(4096)\n",
      "ConnectionResetError: [WinError 10054] 远程主机强迫关闭了一个现有的连接。\n",
      "Exception in callback BaseSelectorEventLoop._read_from_self()\n",
      "handle: <Handle BaseSelectorEventLoop._read_from_self()>\n",
      "Traceback (most recent call last):\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\events.py\", line 80, in _run\n",
      "    self._context.run(self._callback, *self._args)\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\selector_events.py\", line 115, in _read_from_self\n",
      "    data = self._ssock.recv(4096)\n",
      "ConnectionResetError: [WinError 10054] 远程主机强迫关闭了一个现有的连接。\n",
      "Exception in callback BaseSelectorEventLoop._read_from_self()\n",
      "handle: <Handle BaseSelectorEventLoop._read_from_self()>\n",
      "Traceback (most recent call last):\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\events.py\", line 80, in _run\n",
      "    self._context.run(self._callback, *self._args)\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\selector_events.py\", line 115, in _read_from_self\n",
      "    data = self._ssock.recv(4096)\n",
      "ConnectionResetError: [WinError 10054] 远程主机强迫关闭了一个现有的连接。\n",
      "Exception in callback BaseSelectorEventLoop._read_from_self()\n",
      "handle: <Handle BaseSelectorEventLoop._read_from_self()>\n",
      "Traceback (most recent call last):\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\events.py\", line 80, in _run\n",
      "    self._context.run(self._callback, *self._args)\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\selector_events.py\", line 115, in _read_from_self\n",
      "    data = self._ssock.recv(4096)\n",
      "ConnectionResetError: [WinError 10054] 远程主机强迫关闭了一个现有的连接。\n",
      "Exception in callback BaseSelectorEventLoop._read_from_self()\n",
      "handle: <Handle BaseSelectorEventLoop._read_from_self()>\n",
      "Traceback (most recent call last):\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\events.py\", line 80, in _run\n",
      "    self._context.run(self._callback, *self._args)\n",
      "  File \"D:\\1.Notepad\\anaconda3\\anaconda\\lib\\asyncio\\selector_events.py\", line 115, in _read_from_self\n",
      "    data = self._ssock.recv(4096)\n",
      "ConnectionResetError: [WinError 10054] 远程主机强迫关闭了一个现有的连接。\n"
     ]
    }
   ],
   "source": [
    "import sympy.plotting as syp#导入SymPy的绘图模块，并将其别名设置为syp。\n",
    "\n",
    "x,y=sy.symbols(\"x y\",real=True)#定义两个实数符号变量x和y\n",
    "\n",
    "z=x+sy.I*y  #定义复数变量z，其中sy.I是SymPy表示虚数单位的符号。\n",
    "\n",
    "w=sy.cos(z**2).expand(complex=True)#计算复数z的平方：z**2 = (x + iy)**2。然后计算cos(z**2)，这将返回一个复数表达式。expand(complex=True)：展开这个复数表达式\n",
    "print(w)#输出计算得到的复数表达式w\n",
    "\n",
    "wa=sy.Abs(w).expand(complex=True)#sy.Abs(w)：计算复数w的绝对值（模），展开绝对值表达式。\n",
    "\n",
    "syp.plot_implicit(wa**2-1)#绘制|w|^2 = 1的图形，即模的平方等于1。plot_implicit()函数用于绘制隐式方程的图形"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "plot_implicit 是 SymPy 中用于绘制隐式方程图形的函数。隐式方程是指未显式地解出一个变量的方程，例如 F(x,y)=0\n",
    "绘制单位圆的方程 x2+y2-1=0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#隐式方程是一种方程类型，其中变量没有明确地以一个变量的形式出现，而是与其他变量以某种方式隐含地相关"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1b4a368a910>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy as sy\n",
    "import sympy.plotting as syp\n",
    "\n",
    "# 定义符号变量\n",
    "x, y = sy.symbols('x y')\n",
    "\n",
    "# 定义隐式方程\n",
    "equation = x**2 + y**2 - 1\n",
    "\n",
    "# 使用 plot_implicit 绘制\n",
    "syp.plot_implicit(equation, (x, -2, 2), (y, -2, 2), title='Unit Circle', xlabel='x', ylabel='y')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 三维作图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1b4a3ca81c0>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "syp.plot3d((x**2+y**2,(x,-3,3), (y,-3,3)), (x*y, (x,-5,5), (y,-5,5)))#第一个三维图形，表示这是一个抛物面。另一个三维图形，这是一个平面"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1974cd7ce20>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy as sy\n",
    "from sympy.plotting import plot3d\n",
    "\n",
    "# 定义变量\n",
    "x, y = sy.symbols('x y')\n",
    "\n",
    "# 定义函数\n",
    "z = x**2 + y**2\n",
    "\n",
    "# 绘制三维图形\n",
    "plot3d(z, (x, -3, 3), (y, -3, 3))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x19751a2cd60>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy.plotting as syp\n",
    "syp.plot3d(x*y, (x, -5, 5), (y, -5, 5))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "绘制出来的图形会在三维坐标系中显示，并且可以直观地看到这两个函数的形状和交互关系。这对于理解数学中多变量函数的行为非常有帮助"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "本小结作业：用plot_implicit函数 绘制 lemniscate (双环)的方程  （x2+y2)2+2a2(x2-y2)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
